This is a side-tangent from finding alternative third places (the motivation for which I fully support), but I always like to raise this when people bring up the concept: third places are not (and never really were) a thing. It was an ideal invented by a guy who had a very specific idea of what society should look like that was rooted in misogyny and patriarchy. We all should be seeking community, which is what I see in this thread, but from a planning perspective there are much better ways to think about organising our spaces than through the "third place".
Here's a very good video about it by someone far more qualified to talk about it if you want to know more: https://youtu.be/8E5MegoW2pA