Exits from Szith Morcane include:
The Dordrien Crypts. There is a passage leading to the Chasm that leads up to the Dordrien Crypts and then on to the surface world. Heavily guarded on both sides of the Chasm, as per the OP description in our IC thread.
The Chasm. Across, down, or somehow through the Chasm itself. The Chasm is unexplored and largely left alone by the city inhabitants. A very steep descent of an unknown drop into an unknown bottom.
The Lower Bar. The Bazaar has a passageway that leads down below the Bazaar into a cavern and from that cavern, there is a gate through which merchants come and go via a northeastern passageway out of the city. Heavily guarded. Getting in to Szith Morcane is easy. Getting out is more difficult.
I know someone will bring this up, so instead of waiting and then replying, I'll go ahead and say now. "Citizens" normally need a writ to leave the city. Acceptable sources for a writ include one of the city guard officers, the Council, or any of the prominent noble Houses. Tierak Morcane left Desydra's Playhouse without furnishing the writ.