We've never tried something like this at an actual meetup, but contra dancing has become kind of a thing among Boston-area LWers. Two of us were avid dancers to start with, a few more had tried it in the past, and one recently got into it. So now I see a couple of LWers at dances at least once a month.

Advantages: easy to learn, no dance skills needed beyond ability to walk on-beat. The caller tells you what move to do next, so you don't have to improvise if you don't want to. Live music, reasonable cost for an evening (~$7). Lots of eye contact and opportunities for flirting, but not an overtly sexual atmosphere. Find dances near you.