Private Tennis Courts in New York City

I’d like to take up tennis and am looking for a place to take lessons in New York City. Preferably, it’d be a private club where it’s possible to reserve a court to play on—I know there are a lot of public courts around the city, but I don’t want to have to hang out and wait for one to become available. I’ve tried searching, but my Google-fu is failing me and I’m getting too much tennis-related noise. Thanks.

I’ve never played there, but a friend of mine took lessons at Midtown Tennis Club and loved it.

I know nothing about tennis, but I found this list:

In Forest Hills in Queens there’s the West Side Tennis Club, oddly, not on that list. It’s more of a full on country club in terms of membership fees (there’s also a members-only pool, clubhouse and restaurant) but they have 38 courts and the US Open was held there, once upon a time. It’s a very quick walk from the Forest Hills Long Island Railroad stop, which is ~20 minutes from Penn.

By the way, the public courts in Prospect Park and Central Park, both take court reservations:
http://www.nycgovparks.org/sub_permits_and_applications/tennis_permits_renewals.html#reservations