grimwerk: A ceramics class give you lots of opportunities.
You'll be sitting around a large table, facing other people over your work. Class will go for 2 or 3 hours at a time. Your hands are occupied, but you're otherwise free to chat. If you're the quiet sort, it's okay, as others will chatter away and you can jump in when you feel comfortable. Everyone is getting fairly messy, which keeps the mood light. I find that even disastrous clay pieces can look pretty interesting once glazed and fired, so you can feel pretty confident even if you're not too skilled. And if you wind up having a flair for it, well that's just another basis for conversation.
The classes I took were mostly women, but I don't know if that's typical. I suspect it helps if you have a silly rather than serious instructor, as this seems to result in a friendlier atmosphere, one in which people feel okay making jokes and saying odd things.
I'm not the most outgoing of people, and I find it much easier to meet new people if "meeting people" is not the primary purpose of an event. If everyone is building or drawing, then you'll always have a basis for easy conversation. Except Life Drawing classes. Everybody is dead silent when there is a naked person in the room.
edit: Before you sign up, visit a class in session just to see if it is what you expect.
I like your thoughts here. Pottery classes or anything to do with your hands would be similar i guess??. Might try find classes like that myself :)