In some areas, it is definitely significant that libraries have bathrooms and shelter. But the Internet is always a big draw. With more and more of life moving online, libraries are providing an extremely valuable service by making Internet access freely available.
This is most likely true of any large city, but I don't have any first-hand experience beyond those three cities.
In the US, this might be the case. In Sweden, mostly you'll find kids, moms and people studying (depending on the city, if it has a university or not). A very small subset is there for computer access, but it's certainly not a majority.
In Bulgaria, no one seems to go to the library. They check your ID when you go in and it's not really a place to hang out.
Libraries aren't the same everywhere.