What cafes in the city center are open at night?

It depends on which city you're looking in? Because there are late-night cafes almost everywhere, but the list is completely different if we're talking about Moscow or, say, Tver. If you tell me the city, I can give you more specific advice.

In general, late-night cafes are usually concentrated in the center - there's more demand and more people hanging around late. Look for places near the main square, in entertainment districts, or near the train station. Bakeries often work at night, university cafeterias, and shops in malls if they're open 24/7 at all.

The most reliable way is to type the city name into maps or Yandex, filter by "24 hours" or pick a specific evening or night time. You can see reviews there too and figure out if people actually go there at night. Sometimes a place officially says it's open around the clock, but in reality it might close earlier.