Candlekeep Barracks can be found in the south end of Candlekeep.
It is the base of The Candlekeep Watchers.
Loot
If you successfully loot every container in this building you will find:
Side quests
Hull's Sword
Hull asks you to fetch his sword from the barracks. Grab the Antidote while you're in there.
An Errand for Fuller
Fuller has an errand for you. Buy some bolts from the inn. If your reputation is high enough, he'll give you a Dagger +1 in return.
Dreppin's Cow
Dreppin's cow isn't feeling well. Good thing you grabbed that Antidote.