There is no public domain sprite site that I know of.
If you're serious about making your game as good as possible, don't use someone else's sprites. Do one of these:
1. Take the time to practice spriting, and it'll eventually get faster and easier, and in the end you'll be able to be more proud of your project.
2. Make your game with crappy temporary sprites and stick figures. Polish the gameplay as much as you can. Then show it around to some sprite art or game making forums (like this one) and ask if anyone is interested in collaborating with you. Do NOT ask around for artists help with a game that hasn't had some serious work put into it. There are a lot of sprite artists interested in working on projects, but nobody, ever, will offer their help unless they see your efforts first.
A couple good places to start learning to sprite on your own would be
There are tons of tutorials from everything on color palettes to optimizing your workflow, and people will always give you feedback on your work. Likewise, those would be good places to go when you get your game engine up and running smoothly if you want to solicit help.
Protip: Become active in the forums wherever you go before you go pimping out your game looking for contributors. Most places will shun you if you show up and say "Hey, I'm looking for an artist" on your first post.