The Bethpage Park Tennis center was the home of the US Open in 2002. While they can't guarantee that you will play that well, the lessons here are very good. The pros, Steven Kaplan and Keith Kambourian, have developed more top ranked players than any other facility in this region. There are lessons available for adults, juniors and children, as well as a junior development program. Babysitting is available.
They have hard courts and indoor and outdoor red clay courts.