Visit Central/Eastern Europe. These places are a norm in there.
As much as I loved '80s arcades (and wasted way too much money in them), "safe" is not exactly a word I'd use. Many of them, in Italy, quickly became drug markets or money-laundering operations (or both). Arguably, the few surviving ones are even worse today. They were not very healthy either, with no natural light and people smoking.
But yeah, it was a place to go with friends, and I have great memories about those times. Our furious NBAJAM challenges were the stuff of legend.
Edit: I realized I wrote this outside of a small cafe in my neighborhood, with people talking, relaxing on their own, and having breakfast. I consider myself an introvert but always seem to work better in cafes like this, with people around (especially if those people are also working). I always thought it was due to the tentative time limit making me focus better on the task at hand (since it would be rude to stay too long in a cafe), but now I'm wondering if just the proximity to other people might also be helping.
I would be fine with just relaxing in public places like parks without actually having to interact with anyone, unless some people appear to share interests.
Sadly, safe, clean public places seem to be an exception rather than the norm in the world at large, at least from what little I've seen of it.
So we go back inside enclosures that are commercial establishments (coffeehouses, restaurants etc.) in order to be around other people, but interacting with other patrons there is kind of a social taboo.
From my time on the planet I can only think of video game arcades from my childhood as the best examples of places where people got together to have safe fun and often interacted with each other out of choice and had even more fun in doing so.