If you don't want to do the clinics, see if you can get to the pro shop at Van der Meer at Tennis center, not Shipyards. They keep a book with players looking for games. You can either copy some names, enter yours, or any combination. Very serious tennis happens there.
It's hard to get on the plantations; Shipyards and Palmetto Dunes, e.g. but you can pay $5 and get a "day pass" to Sea Pines.