Cindi,

Have you searched your area via google? I live in Austin and we have a strong Chinese community. We have the Austin Chinese School which meets on the weekend. My understanding is this is a norm. All my friends that are Chinese send their children to that school and it is for anyone.

The other suggestions of local universities is a great one and a lot of them allow for auditing or at least you should talk to the schools so they can direct you in the right direction.