I had a great time with Salsa dancing. In the right place, you dance with lots of different girls all evening long. Since you can take classes, you can get reasonably good at it so as to make a good impression. Lots of girls will dance, some won't, but because each song only lasts so long, you can meet lots of people. Furthermore, it's fun in its own right, nice music, doesn't cost much, and you can learn a surprising amount about someone from 2 or 3 minutes of dancing with them.
I was going to post the same thing. Another plus is that the salsa community is filled with classy and smart people (it takes a surprising amount of brainpower to dance well -- many of the best leaders are techies).