Bars are notable for staying open late, but I’m not really familiar with alternatives that might operate similarly. I think many cafés (at least around my area) tend to close a few hours earlier by comparison, which would be my go-to for an alternative otherwise, so what other options are there?
Dance clubs. Most have alcohol available but it isn’t a required part of the experience. The people I know who go out dancing the most don’t drink.
But it depends what you’re looking for. If being near alcohol in any way would be a problem, that changes things.