Probably one of the most socially friendly places I recall in recent years was a CrossFit gym. I know people shit in them as being full of cultish twats, and to some extent I won't argue that, but compared to a standard gym there's quite a 'us' rather than 'me' vibe to it. Find those kind of places where people look to support and improve each other rather than show off what they know or can do.

Though I'm about the least socially apt person around one thing that really has stuck out to me, don't go there with a goal other than to do the thing. If you go with the goal of a date you're gonna be disappointed, go with the intent of doing what you like instead.