We've found some great sitters through care.com. I tried sittercity.com too but never got many responses.
I find with care.com that you can find great people but you need to have patience. For every 5 responses I would get, only 2 or 3 would actually set up an interview and probably only 1 would actually show up for the interview. That said, I like the simplicity of having someone else deal with the background check for you. We had people come to our home for interviews and actually paid more attention to how DS acted around them then what they said. We have a new woman starting on Saturday. After the interview she got up to put her coat on and DS burst into tears and ran to her to be picked up so he apparently likes her :)
But we've previously used two sitters from the same sight and both were reliable, professional and great with DS. I know it's very scary but it seems like you'll be around a bit. Just interview and choose someone and spend the first few times they're there cleaning and doing something within earshot and work up to actually leaving. You'll be okay :)