The City has dungeons, both of the underground cell kind, but also of the generic underground adventuring complex kind.
The City has plenty of sewers, transporting the waste of the city to the river or to underground streams. Some of the sewer lines are huge, servicing hundreds of thousands of people. Some are in ruins, reflecting the state of the landscape above. Wererats, smugglers, cultists and thieves have their hideouts down here.
The City has cellars, some of which are huge winding complexes. Tunnels may run from cellar to cellar, connecting various structures on the surface. In some places they will connect to the sewers. Cultists of ill favored gods will hide their temples below ground in these structures, and use the many entrances to enter and exit unseen. In the abandoned parts of the city, these cellars will form dungeons like any other underground complex, harboring those creatures that avoid the sun.
The City has catacombs. Though there are churchyards and necropolises on the surface, these are hardly large enough to hold all the dead of the City. People have gone below ground for an answer, and vast catacombs can be found beneath temples and aforementioned necropolises. Merchant families and nobles may have their own private tombs beneath their ancestral homes. With every dead, the catacombs are expanded a bit more. Many parts are entirely forgotten, inhabited only by the ancient remains of people that have gone long before. And by those that have arisen to undeath, either spontaneously or by the callings of a powerful necromancer or coven of death cultists.
The City has hideouts. Connected to the sewers or cellars, or hidden under one of the city's many structures, the City has many underground complexes, built to house objects or people far from the sight of the people above. Thieves guilds have expanded on their underground complexes for centuries. Temples have constructed elaborate vaults to hide forbidden artifacts. Eccentric merchants have built grand tombs, the location of which is known only by themselves and the dead craftsmen within.
And the City has dungeons. Whether belonging to the Inquisitors, the military forts, or local lords, these dark dank complexes of cells and corridors stretch far and wide. Generations of prisoners have been born, lived and died within. Some even say that there are parts of the inquisitors dungeons that have not been visited by outsiders for decades, but still host prisoners inside. Though whether they remain human is a point of contention.