The closest thing I've ever seen to a teen center was a sports facility that had a room for kids and teens to hang out, but that was closer to a babysitting service. Paired with the facts that you had to pay monthly membership dues ($25 to $100/mo these days, apparently) and the whole facility was meant for something else entirely, it's not something I would first describe as a teen center. Not any more than I'd call a high school a chemical R&D facility just because of its chemistry classroom.

Outside of that one room, I'm not aware of anything else nearby me that would be even remotely similar.