Much of Kadara Slums was glossed over during the main walkthrough for the simple fact that you never really need to bother with it during the quest "Hunting the Archon", or any subsequent Priority Ops. For the purposes of exploring and questing Kadara, however, it’s worth a bit more attention. At the southeastern end of Kadara Slums you’ll find the lift that leads to Kadara port, where you’ll start out. At the northern end of the slums is the Warden’s office, and the fence that separates Kadara Slums from the badlands.
The most interesting bits of the Kadara Slums, however, is the building complex to the west, the majority of which is composed of Tartarus. Of course, calling anything besides Tartarus a "building" is probably too generous, as most of the multi-leveled jumble consists of stairs, pre-fabricated metal floor plates, and shipping crates that have been repurposed as shelters.
Outside of Tartarus, there’s precious little to see in the Slums. Up on the highest level of the building complex, against the southern edge of the slums you’ll find another proper shelter, which just so happens to house an Outcast guard room, which has a Terminal you can read and an Outcast Guard you can gossip with.
Also along the southern side of the building complex, but in a shipping crate in a lower level you’ll find Dr. Nakamoto, who will give you the quest "Modern Medicine". If you head west from the crate the good doctor runs his clinic out of you can turn north and leap into a higher crate out of which a Black Market Dealer runs shop. Are there even any laws in Kadara? If not, how can you have a black market? Whatever, this shifty Salarian will sell a variety of consumables… all of which you can buy quite legally from other sources. You can also find a shipping crate serving as an Oblivion den on the ground floor and a corpse behind some crates in another shipping container further west.
Make your way over to the Tartarus building and search the ground floor north of the building’s exterior to find two Looters picking at a Salarian corpse. Scan the corpse if you wish and confront the looters, who care little for your morality. Upon on the second floor of the structure surrounding the bar you’ll find a Disillusioned Outlaw who will suggest you familiarize yourself with Outlaw weaponry, starting the quest "Task: Outlaw Weapon Crafting". The last thing to do before you enter Tartarus is explore the dark alley north of the bar to find a corpse and a Datapad. If you scan the latter and read the former you can complete the quest "Task: Traitor or Victim", even if you haven’t started it yet!
Enter Tartarus and on the ground floor you’ll find the bartender Kian Dagher, who will chat with you a bit. In the northwestern corner of the bar is a Salarian named Derc, who will give you the quest "The Baryte Rush". Upstairs you can talk to a woman named Cassandra Verner, while through a door to the west you’ll find Reyes Vidal.
Did You Know?: Cassandra Verner mentions her brother Conrad Verner, who annoyingly idolized and emulated Commander Shepard to his own detriment in the original trilogy. Cassandra Verner seems to be similarly enthralled with Sloane Kelly.
Lots of quests to start here in the Slums, and you’ll be coming back to complete or update several, but otherwise there’s little to recommend this place. You can search around for the odd Iridium or Uranium deposit, as well as a few containers to loot.