I think the sites used to be better. I used to have a lot of luck with okcupid, but they changed the way that the messaging system works, so both parties have to agree to the contact to get to send any messages, which means that just getting a message across is practically impossible. I went from getting most of my messages responded to, to getting none of them responded to when they made that change. (obviously YMMV, but I was one of the most effective accounts in the system for the number of responses I got per attempt, even most ND are lucky to get a quarter of the interest)
I haven't tried any of the dating sites for autistic people, so I have no idea how well that works.
Depending upon your budget and how important this is to you, there's also matchmakers and just hiring a wingwoman/wingman to help go out and meet somebody. A good wingwoman/wingman will be able to help with the social skills aspect of meeting somebody, even if it's ultimately unsuccessful, she should at least give some indication of what to work on.
A wingwoman/wingman is probably the way to go if you can find the money, and have a good one in the area. They can address the more practical things that can't really be practiced with a therapist, so even if the outing is a bust, you should walk away in a better position to try again on your own.