The Wink and Tickle
Your first stop should be this brothel near the main gates. Talk to Bela about the city's problems, then head upstairs, where three quests can be started. First, speak with Erb. The halfling wants his ring back from Lady Jadale before her husband returns. Next, speak with Yvette (you'll have to open some doors to speak with the working ladies). She'll ask you to help her rescue her baby, taken by Garlone who lives in the slums.
As Bela told you, one of the courtesans will give you some information on the captains. If you're female, speak with Oreth. Males should visit Rhaine. They will give you the keys to Kurth's and Baram's compounds if you agree to kill them.
Garlone's House
You won't have much trouble convincing Garlone to give you Yvette's baby--you just need to show him some coin. He'll want 1000 gold but will take 250 if you threaten him. Make sure you check your inventory to see the baby nestled among the potions, rings, and books.
Lady Jadale's Estate
Lady Jadale doesn't want to give up Erb's ring. Erb loves her, and she knows it. Appeal to her love of Erb--tell her that he wants the ring back so that her husband won't hurt him. She'll relent and hand it over. Alternately, you can lie to her about the legality of the ring, or you can just buy it from her for 1000 gold or talk her down to 400 or 250, depending on your persuasion skill.
The Cutlass Inn
Two rescue missions await you here. Baram has kidnapped Londa's nine children, and she wants them back. Elynwyd has also lost a loved one--his sister Evaine has been taken by Kurth, and he'll give you his signet ring so that she'll trust you.
Equipment
There are a few places to buy stuff. There's the Priest of Tyr at the temple, a shady character at the northern wall, and a smithy and general merchant in the city center.
Colmarr's Fantabulous Contraptions and Magical Errata sells a variety of good equipment. It's run by a gnome inventor. He's developed a machine that turns sewage into potions, but it's broken. Find the three missing levers and fix the machine, and you can use it. The Lever of Stone can be found in a chest on the first floor of the Wink and Tickle, the Lever of Wind is in a chest in the sewers, and the Lever of Water will be given to you by the outcast ghoul in the sewers.