Go to USTA's website and use their It's Your Game
feature. It should be in the upper left hand corner of that page. Select find a partner or court and it'll ask you for your zip code. I think you have to register (yourself) but I also think it's free. Since I play at a Club...I haven't had to use it...but it's a place to start.
Another option is to find out who is a USTA League Coordinator for your area. Those folks are excellent resource people and can tell the "hotspots" for both "pickup" play as well as more organized ventures.