I'm sitting in the nearest coffee shop to where I live, which happens to be a Starbucks. When I walked in, the manager said "Good morning, Matt."
I've only been coming here a few months, one or two times a week, but it now it feels a bit like home.
— you may be looking for a different type of third place rec though, a place where you can definitely build community, and there's no guarantee of that at a coffee shop.
My impulse for me is to assume I'm not alone in this need/desire and to start something. Any place can become that third place, now the challenge is just getting people to join you there.
While still in college, I plastered "reading aloud night" posters around the campus and invited people to bring something to read aloud to others: either their own work or a favorite snippet from another author. A half dozen people came and we hung out until late in a common area—and then kept doing it. Some beautiful friendships started in that little group.