There are plenty of public places in the US, but the so-called "public square" where strangers gather to debate is a total myth. It does not exist anywhere, and I'm not sure it ever has existed. Certainly not in my lifetime, anywhere I've ever lived.
Friends do gather in public squares to talk or lounge or listen to concerts or whatever. But the kind of thing that happens on Twitter, or on HN for that matter, does not happen IRL. Occasionally there's a crazy preacher who attempts to address a crowd of strangers, but mostly the crazy preachers get ignored or ridiculed. There's no real, serious discussion and debate in the public squares among people who didn't already know each other.
You can go to an open city council meeting to discuss and debate public issues, but those meetings are strictly governed by rules and moderated.