If you can skate, try an ice skating rink. Or roller, if that's more your thing. I know one girl somewhat from ice skating, which I guess is pretty good cuz I don't like, do much else social anymore. Either that, or dance classes and the like would probably be good.
Could also try gyms, but gyms are in a lot of ways replacing bars for hookup spots. Which I don't like much at all, but it's the way things are now. If you wanna meet a ton of girls, go like, 5-6PM, as it's after work. If you want to avoid all the bros at the gym, go to aerobics class, as they're populated by females, and usually most guys there are...not cool. So, if you're worried about your coolness, for better or worse, you'll fit in...or stand out...or something.
Lastly, an easy place too would be if you're into video games, anime, board gaming, as it seems 90%+ of Aspies are, then see if you can find an anime club or something of that nature in your area. I don't know, I feel like I outgrew that "crowd" of people, but still totally love anime and the related things, but I find that crowd of people annoying now for the most part. Girls ARE there, but the ratio is usually like 1 girl to 5 guys, so it's kinda a lot of competition, really, as all the other guys have the exact same thought process as you.
Those are my suggestions, from a guy who's 20, and hasn't had a girlfriend in his life, so take it for what you want.