The Tenement of Thugs

 

 

It's very hard to kill all the thugs, so you might as well take Sybil's advice and use the key to open the back door.  You can find the key on the 3rd floor after you kill the Mage Thug.

The secret door at the bottom will let you sneak past the thugs.

This will take you out to the Alley of Lingering Sighs.