Once you arrive on Coruscant the very first thing you'll want to do is pick up the quest "Crisis in Galactic City" from Anitol Rosspar. Once you have that head north towards the Senate Plaza stopping quarter way up at the Taxi Terminal and then again slightly further up at your class related NPC to accept your "Advanced Training" quest. If you're not level 10 this might not be available to you right now, if it is not come back after you do what you need to do in the Senate Tower. If it is stop at the Commerce Hall and turn in your quest as well as pick your classes Advanced Specialization.
Also while you're in the Commerce Hall be sure to talk to all the Crew Skill trainers not only for the Codex entries and XP but to also grab Crew Skills before you leave.
Anyway, whichever order you do that in, up north you will want to update your quest "Crisis in Galactic City" so it has you talk to Captain Winborn as the next objective. Also while you're up here update your class quest so it has you going to the same place as your other quest. With this out of the way you will want to head south back to the flight master and fly to the Old Galactic Market.
Once you arrive in th Old Galactic Market you'll want to gather all the quests you come across on your way to the "Crisis in Galactic City" quest objective. When you arrive at Captain Winborn you should have the following quests available to you: "Crisis in Galactic City", "The Senator's Stolen Goods", "For Better or Worse" and your Class Quest. We'll be starting with "Crisis In Galactic City".
Crisis in Galactic City
Repair 3 Secure Network Access Nodes
You can find these all around the edges of the Shipping and Receiving Docks, just look for the glowing blue computer panels that are broken. There is a long Bonus Quest tied to this one that requires you to kill a lot of the Guild Forces in the area. The bonus quest is as straight forward as can be, just check your map each time it updates to figure out what to do next.
The Senator's Stolen Goods
Retrieve 7 Stolen Chips
The Stolen Chips you need for this quest can be found all around the area it shows on the map, just look for the long glowing blue crates. As with Crisis in Galactic City, this quest has a long bonus tied to it as well. Also, much like the Crisis in Galactic City quest if you follow the locations on your map for this quest it is a breeze.
Do this either before or after "For Better or Worse" depending on where you have to go for it.
For Better or Worse
Search the Dancer's Quarters
Very easy quest, the location you need to go to for it is marked clearly on your map.
After you complete these quests use your Quick Travel ability to return to the terminal at the Old Galactic Market and turn in your quests. On your way back to the NPC that gave you the Crisis In Galactic City Quest you will come across "Officer Anstiss" who has a quest available for you called "Cantina Contusions". This is an extremely easy quest, the locations are marked clearly for you on your map. Also while you're in the Inn, if you can talk to your Companion do so as the quest for interacting with him rewards XP.
Speak with Zooki
Extremely easy, turn it in after you finish.
After turning in all of your quests accept the only followup "Crisis in Galactic City". You now have to return to Minister Imogh in the Senate Tower, so fly back to Senate Plaza and head north. On your way north be sure to stop at Spirakris Zarem and accept the quest she has, "The Politics of Dissent". This quest is done in the Senate Tower, it's extremely easy and just requires talking so you'll want to get it out of the way at the same time as Crisis in Galactic City. While doing The Politics of Dissent quest be sure to get and update the "Gree: Hydrosupply Leak" quest across the hall.
Two more things to do. One of them is refresh your class quest, what I mean by refresh is turn it in and accept the followup. After you do that in the same general area you'll see Senator Nalrin Daheel who has a quest for you, "Follow the Money". Accept this and head back south to the Senate Plaza. Stop at your trainer in the Senate Commercial District and train your new abilities. Stop back at Spirakris Zarem and turn in your quest to her and accept the quest from Agent Nurls Yorksin before continuing south to the Taxi Path and flying to Black Sun Territory.
NOTE: Jedi Knights will have to speak with Kira Carsen first and complete this part of their class quest before proceeding to the Black Sun Territory. Also they will be unable to accept "The Freightskippers" before they complete their class quest.
Once you arrive in Black Sun Territory grab all of the quests and the Quick Travel terminal in town before taking the southern elevator down and going killin'. The quests you should have available to you are "Follow the Money", "The Pickup", "Gree: Hydrosupply Leak", "The Freightskippers" and of course your Class Quest. We'll be starting with "Follow The Money"
Follow The Money
Retrieve 8 Stacks of Kavin Bills
The Black Sun Forces in the area are who you need to kill for all 8 Stacks of Kavin Bills. Do this quest at the same time as the bonus quest below:
The Freightskippers + Bonus Quest "Freightskipper Fracas"
Eliminate 18 Black Sun Forces
For The Freightskippers quest you need to kill a Black Sun Loader Droid, they're easy to find as they're the only hostile "silver con" droid in the area. As for the bonus, you will want to get stage 1 and stage 2 of this bonus out of the way asap since the updated bonus has you killing the Black Sun Forces in a different location.
- - - On your way west to the next quest, "Gree: Hydrosupply Leak" you will come across another NPC with a quest, Captain Theraguin. He has the quest "Boom" which we'll be doing later. - - -
Gree: Hydrosupply Leak
Shut Off the Southeast, Southwest and South Hydrosupply Flow Valve
Each of the three Hydrosupply Flow Valves are marked clearly on your map, you won't have any trouble finding them. While you're down here be sure to do the bonus tied into this quest, requiring you to kill 12 of the Black Sun Forces down here.
Speak to Deringon Lobacc
Easy quest, he is marked clearly on your map. Speak with him to complete the quest.
- - - Before you get to the area where the next two quests take place you'll find an NPC, Agent Folaris who has the quest "Partial Eclipse". Accept this, we'll be doing it in a bit. - - -
Disarm 8 Booby-trapped Supply Crates
This is a very easy quest, each of the supply crates are glowing blue, first time you use them you disarm them and then the second time you loot the ordinance inside.
Stage 3 Freightskipper Fracas (Bonus)
Defeat 3 Black Sun Gang Leaders
The Black Sun Gang Leaders can be found all over the area. Very easy quest in other words.
Get this out of the way either before or after "The Freightskippers" depending on where your class quest is.
Shut Down 4 Tracing Equipment
Another extremely easy quest. All of the Tracing Equipment is in a single room and glowing blue. Shut it all down and you're all done!
Locate the Stolen Freight
For this quest you need to tag the Stolen Cargo once you enter the room it shows on the map. Very easy, all of the crates are glowing blue, just right click them to tag it.
Final Stage - Freightskipper Fracas
Recover Stolen Shipping Manifests from Teven Liss'ard
He is pointed out very clearly on your map, kill him and loot the Stolen Shipping Manifests
After you complete all of your quests you will want to return to Agent Folaris and turn in your quest and then head all the way north to Captain Theraguin and turn in your quest to him as well. After you do this return to town and turn in the quests that need to be turned in here as well as accept the new quest from Lieutenant Doorn. After you do that fly back to Senate Plaza (up north) and turn in all the quests you have here as well as accept any new ones. Also don't forget to train before you leave this area!
You should have the following quests once you've turned everything in and accepted all the followups: "Gree: Ugnaught Saboteurs", "Secret Passages" and your Class Quest.
Once you're done in the Senate Plaza area of Coruscant it's time to go back to killling! Head back down to the Taxi Terminal and fly to the Justicar Territory.
Once you arrive in the Justicar Territory you will want to grab the Quick Travel Terminal thingy and then head directly west to Agent Jaffkee who has a quest for you called "White Noise". After you've accepted that continue south to another set of quests. Here you'll find Renalda Agareth who has the quest "Justicar Injustice" and also Luran Gonthor who has the quest "[Heroic 4] Trouble in Deed". You won't be able to solo the Heroic 4 but people are constantly looking for other players to run it so it's a very real possibility you can find a group for it. After you've got these two quests it's time to get started.
Install Anti-jamming Device Alpha
Marked on your map, it's the only one you can do for now.
Speak to Fieler Dan
She is marked clearly on your map, talk to her and update your quest.
Install Anti-jamming Device Echo
- - - Across the hall from where you have to install this jamming device are two quests. One from Paus and another from Reid Gandon, accept both of them. - - -
Stage 1 - Justicar Resistance (Bonus)
Defeat 15 Justicar Forces
Get this quest out of the way now before heading north to the final White Noise Objective.
Install Anti-jamming Device Delta
This is the final step of White Noise, install this Anti-jamming Device and continue to the next quest, A Diverting Assignment.
A Diverting Assignment
Retrieve Manifest Data Packets 001, 002, 003
Each of these three locations are marked clearly on your map. Head to each of them and retrieve the Data Packets that you need for this quest. Also while you're doing this quest be sure to do the bonus which has you kill 30 Justicars.
Gree: Ugnaught Saboteurs
Search for Ugnaughts
This is just the first part of the quest, it continues later on but for this part you need to go down the elevator and speak to the Ugnaughts down in this room. Depending on if you pick the light or dark side during this conversation will determine what you have to do for the next step. I chose light so if you want the same quest as me for the next part choose that option too. (The Dark side option isn't that much different so don't worry if you'd prefer to choose that. In fact Dark Side is easier).
Obtain a Justicar Security Belt
For this part of the quest you need to kill a Justicar Heavy Gunner, which is a silver con mob in either area that it shows you can complete this quest.
Stage 2 - Justicar Resistance (Bonus)
Defeat 45 Justicar Forces
Do this before leaving this area.
Download the Schematics
Head to where it shows you on the quest and kill the gold con in the way of the terminal. Use the terminal to download the Schematics and you're all done.
Final Stage - Justicar Resistance (Bonus)
Recover Access Codes from Jessa Bo'den
She is marked on your map right near the Secret Passages objective. Kill her and loot the codes.
Destroy the field Generator
Once you enter the Justicar Security Office the rest of the quest is clearly marked on your map.
Killed in Custody
Retrieve a Droid Memory Core
Kill a Droid inside the Justicar Detention Center to get the Memory Core and then use it on the terminal. Also while you're on this quest be sure to do "Prison Punishment" which is a bonus that requires you to defeat 8 Justicar Prison Defenders.
Get this done before you return to turn in any of your quests.
I find it easiest to just Quick Travel back to town and start turning in your quests as you head further west. The first quest gets turned in at the Mission Dropbox, the second to Agent Jaffkee and then all the remaining ones to the south in this small little area. After you turn in all of your quests you'll want to head to the far south where The Works Elevator is. Here you'll find Fez Burba. Talk to him and accept his quest "Planetary Checkup" before proceeding to the elevator and riding it down to The Works.
This is pretty much the second to last area of Coruscant, all that's left after this is the Jedi Temple although The Works and the Jedi Temple are pretty much connected. Once you arrive in The Works grab the two available quests and the Quick Travel Terminal that is here. Before leaving the little town area at The Works you should have the following quests available to you: "Gree" Power Outage", "Planetary Checkup", "Meltdown!", "Core Dump" and your Class Quest. Now, let's get started.
Scan the Primary Junction Room Access Pipe
We're only doing this part for now.
Collect 5 Rogue Droid Memory Cores
Very easy quest, these drop from the Droids in the area where you're going to be doing the Bonus quest (listed below).
Stage 1 - Enemy Droid-machines (Bonus)
Defeat 15 Rogue Droids
Do this on your way to the Gree: Power Outage quest and make sure it's finished before doing anything else.
Gree: Power Outage
Repair the far northern Power Conduit
Stage 2 - Enemy Droid-machines (Bonus)
Defeat 30 Rogue Droids
Do this part on your way to the next quest and then on your way back to another quest. Not all the Rogue Droids count for this quest, it's annoying but important to do.
Release Control Valve TE-883, TE-637, TE-512, TE-281
Easy quest, all of the Control Valves are around the room it shows on the map for this quest. Look for the glowing blue computer panels.
Scan the Thermal Exchange Room Access Pipe
Scan this pipe while you complete Meltdown!
Gree: Power Outage
Repair the nearby Power Conduit
After you scan the Power Conduit for Gree: Power Outage you'll want to head back north. You need to take a different route up here to get to the next set of quests and also before you do that you need to complete Stage 2 - Enemy Droid-machines. This is an annoying quest to do but very neccessary so you don't fall behind in level. After you get this out of the way and unlock the next stage you will want to complete it before proceeding southwest to the next quests.
- - - On your way south to the next quest you will come across Ensign Belkan who has the quest "[Heroic 4] Enemies of the Republic". Much like the Trouble in Deed quest, this one is frequently run by players so grabbing it incase you need it while in the Jedi Temple isn't a bad idea. - - -
Core Complications (Bonus)
Defeat 12 Imperial Forces
After you pass Ensign Belkan you will start running into Imperial Forces. Kill 12 of them for this bonus quest which is tied into Core Dump.
Scan the Secondary Coupling Station Access Pipe
This is the final thing you need to do for this quest before being able to turn it in.
Gree: Power Outage
Repair the final Power Conduit
After you repair the final Power Conduit continue west to the Taxi Pad area. Turn in both quests here and then take the Speeder to the Jedi Temple Ruins to do your Class Quest.
Not everyone has a Class Quest at the Ruins of the Jedi Temple, if I remember correctly... only Jedi's do!
On your way to the Jedi Temple elevator you will come across a Sealed Door which when you open it an NPC will walk out and give you a quest, "Insult to Injury".
Insult to Injury
Defeat the Imperial Commandos for Jedi Master Starsnow's Journal. Also do the bonus quest here which requires you to kill 10 Imperials.
Finish this quest now.
After you complete your class quest Quick Travel back to The Works Sector and turn in the quest you have for here. Ride the elevator up and turn in your quest to Fez Burba before heading over to the Taxi Terminal and flying to the Black Sun Territory. In the Black Sun Territory you will want to turn in your quest to Lieutenant Doorn (Anyone else keep thinking it's Lieutenant Dan? I keep hearing Lieutenant Dan Icecream!!!! In my head...). After you turn in your quest to him fly back to the Senate Plaza and finish up turning in what you have for here.
After you turn in all of your quests you will unlock your ship and the next quest (your class quest) which requires you to use the Holoterminal on your ship. Be sure to train before you head to your ship. Once on your ship use the Holoterminal to update your class quest and then fly to Taris, the very next planet you're going to be questing on.