The city in Dark City is also Tim Burton's Gotham

https://www.reddit.com/r/FanTheories/comments/5ldggx/the_city_in_dark_city_is_also_tim_burtons_gotham/

Gotham City in Tim Burton's Batman movies is perpetually dark and rainy. Most of the buildings appear to be art-deco models built more for style than functionality. There are a lot of older-model cars, and people tend to dress in older styles.

All of the same can be seen in Dark City.

In addition, Batman/Bruce Wayne changes appearance in nearly every movie. The billionaire is a minor celebrity, but no one seems to notice when he changes. This could be because the Sleepers are simply putting someone else into that role, and rewriting everyone's memories so that no one notices the switch.

So, Gotham is set in a corner of The City, where the Sleepers are experimenting with the idea of a costumed vigilante fighting over-the-top criminals.