Belsavis Daily Quests (Republic) - Republic Wilderness Outpost
Restraining the Darkness
For this quest you will be required to recover the Ancient Devices from the Imperial Looters in the area. After you collect all of the Ancient Devices required for the quest you will be required to use them in destroying the Imperial Ship nearby. Even though the quest and Torhead both say to go inside the tomb area thing, all of the looters that you need to kill are outside. Of course there are some inside but why waste time going in there when you don't have to.
The bonus quest requires you to kill 15 Sith in the area, I usually skip this one unless I am really close to completing it by the time I get all the Ancient Devices.
This quest awards you with 1 
Daily Commendation
Strengthening The Chain
This quest requires you to kill 3 Rattataki Leaders. Very easy to do just there aren't many of them so if someone else is here you'll probably want to group up for them. The bonus quest here requires you to destroy 4 crates in the area. Also in the dead center of this area under the large tent there is a security chest.
This quest awards you with 1 Daily Commendation
After finishing these quests you will unlock the next one:
Emergent Medicine
For this quest you are required to kill Greater and Scavenging Rift Lurkers for 8 Venom Glands.
This quest awards you with 1 Daily Commendation
Melt'water Outpost
[Heroic 4] Open Communications
This quest awards you with 3 Daily Commendation
[Heroic 2+] A Lesson is Learned
This quest awards you with 3 Daily Commendation
Oasis Republic Station
[Heroic 4] The Statis Generator
This quest awards you with 3 Daily Commendation
Riot
This quest requires you to kill 15 Rakata and also free 4 of their slaves. The Rakata are all in a tunnel east of the Oasis Republic Station right nearby the Rakata Teleporter that you come in on if you port up north from the Melt'water Outpost down south.
This quest awards you with 1 Daily Commendation
Unheard Frequencies
This quest has you killing the droids inside Stasis Vault 113 for 4 Memory Cores. All of the droids in here have a chance to drop them so it doesn't matter who you kill. However, there are a lot of Slicing nodes throughout this area as well as a Security Chest in the back, so keep that in mind while you're doing the quest here. I usually kill my way to the back, grab the chest and then run out before anything respawns.
This quest awards you with 1 Daily Commendation
Sleeping Rakata
This is a multi stage quest that starts with having go to Elshuu's Prison Chamber. On your way here you will have a Bonus Mission available to you that requires you to kill 15 of Elshuu's Followers. I usually skip this Bonus Mission but only because I have stealth, otherwise I would do it every time since you pretty much run into all 15 of them on your way to Elshuu's Prison Chamber. Once you're here you will need to kill the three Disciples of Elshuu and then use the little crystal here.
Once you do that you'll be teleported to a... different place to say the least. Once here you will want to talk to the only NPC that you see and provoke him into a fight. Kill him and then you're all done.
This quest awards you with 1 Daily Commendation
Prison Repairs
This quest requires you to defeat the Esh-ka Forces in the Transporter Control Center area off of northern The Tomb and also deactivate the Transporter Controls. This is a very easy mission with no bonus mission attached to it. The Esh-ka in here are very squishy from what I've seen and drop a decent amount of credits. Also there are quite a few Slicing nodes in here if you have that gathering Crew Skill.
In addition, in the vertical hall to the west you will find a Security Chest all the way up north guarded by an easy to kill level 50 elite. Taking him out will allow you to collect your goodies. That's really just about all the important information I can give you about this quest.
This quest awards you with 1 Daily Commendation
Containing The Beast
You get this daily from outside The Greater Menagerie area from a little control panel. Before actually doing the quest you're required to collect the Welding Torch from a crate just to the northeast of where you get this daily. Once you have the torch you'll want to kill your way through The Greater Menagerie area (you can do the Bonus Quest if you want, I usually skip it but then again I can stealth past all of the enemies).
Once you go through the group phase in here you'll want to make your way over to the door which behind it you'll see the giant beast you need to seal in. Right click the three little blue circles that light up to seal him in and that's all there is to it!
This quest awards you with 1 Daily Commendation