Crown City Without A King - Kingsglaive Base Camp
First Available: Chapter 15
Other Requirements: Royal Edition DLC
Location: Insomnia Kingsglaive Base Camp
Rewards: 1,000 EXP & The Clever's Talisman
This quest is part of the Final Fantasy 15 Royal Edition DLC; without that DLC this as well as much of the extra stuff in Insomnia will be unavailable. For this quest what you have to do is go to multiple different areas throughout Insomnia and take pictures of the objects you're told to.
At each of the quest marker locations on your map when you press whatever your "action" button is you'll get a prompt that tells you what you have to photograph. Unlike many of the other quests in FF15 that involve taking pictures, you'll have to do these ones manually by opening the item menu and selecting your Camera.
If you're having trouble getting the quest to update for one of the pictures you took then try zooming out and getting more of the area in the picture. Completion of this quest as well as Relics of the Empire and A Glaive Out of Time quests will reward you with an extremely powerful accessory for one of your bros. Make sure to go into your inventory and equip it immediately (yes, it's that good).