I tend to be attracted to "awkward" girls, for lack of a better descriptor. I don't care what their diagnosis, but girls who can share the experience of finding social interaction difficult (or tedious) are appealing. Most "normal" girls seem to place a high emphasis on being social, so I struggle to meet that need as well as the need to do so for her friends and family. It also helps to be with someone who can understand that you are different, and not judge you for being that way, or try to change you, or read into things wrongly. Much like I assume NT couples can read each other, two people with similar frustrations and expectations can better relate to each other. It's the basis of most "support groups," and what are relationships, but mini support groups we establish in order to find other people we can relate with. Relating is the root of the very word.
Most of my relationships have been with "normal" girls, though, since there are so few aspie women. I've dated one, but the timing apparently was wrong, as she was mired in a lot of other issues.
I'm beginning to suspect that I'll never find a girl I can completely relate to, as I've never met one yet. It frustrates me, because I'm sure there are dozens of girls out there that would be perfect for me, but I'll probably never meet them.