Roman Pompeii, at least, seems to have had a thriving nightlife in the districts where the wine bars, or popinae, operated. The popina sells light fare like olives or cheese, but if you've been kicked out or want something hot, the same district is bound to have at least a few streetfront food stands, or thermopolium which serve hot food out of ceramic dishes in the counter.

You can actually get an idea what these looked like, as we're fortunate enough to have remains of a Pompeiian thermopolium in relatively good condition.

There's a ton of popular history coverage of Roman bars and street food, but the only scholarly source I have close at hand is a relatively brief discussion by Ray Laurence in Roman Pompeii: Space and Society. He's mostly concerned with the disreputable reputation of these bar districts, and attempts to regulate their gambling and general sordidness. I selfishly hope somebody comes along here to drop some juicy primary sources on us.