The Cafe Mediterraneum[0] in Berkeley retained this kind of atmosphere until a few years ago (money issues from what I heard.)
I hung out there on a daily basis for a year or so, and it was like I'd finally found the social environment designed for me: I could go in and just read, or work on whatever I was working on—and typically before long I'd be joined by someone from a fairly large ring of folks who knew each other to varying degrees. There was a kernel of us who all knew each other very well (many had known each other for years or decades even), and then a larger outer circle who would sometimes join in or not but were always around.
Occasionally you'd strike up conversation with someone new just because you both had been showing up regularly for a while, and associating with some common people, "Hi, I'm XXX—I see you've been talking with YYY recently. What are those books you have there?" (If you were showing up regularly enough, then you were becoming a "Med Head," which meant you probably had enough in common with any other Med Head that an interesting / amicable conversation would likely result.)
There was a rhythm through the week and month when traffic patterns changed or periodic events were held (e.g. Tango night once a month). We knew all the staff and the owner, and at least bits about the life stories and work of a group of regulars numbering somewhere around... 30 maybe? As much as our conversations might be about philosophy, literature, linguistics, mathematics, etc.—they were as often just gossip related to the community there or around town.
If you were talking about something that sounded interesting, it was not uncommon for people at nearby tables to chime in, and if that was going well we might join our tables together and continue. It was open until midnight and we'd almost always stay until then, often chatting more rather than working as the time got later. At some point people would pick up instruments or someone would hop on the piano and improvise something while the rest of us continued talking. Maybe a couple times a month a couple of us would order a beer from behind the counter as the night was ending. Several nights a week a group of us would go on a walk around town after closing.
Since then, I've considered the existence of a place like that to be the biggest draw to living somewhere—but I haven't had much luck finding it. I was optimistic that Cambridge (MA) would have something, but I never found it.
[0] https://en.wikipedia.org/wiki/Caffe_Mediterraneum