If you want a wide, electric/water site on the beach with individual picnic tables in a concrete shelter, try Goose Island State Park across the Copano Bay bridge from Rockport. You also have a choice of shaded sites in the live oak trees, but we chose a beach site (we don't have many ocean beaches in Colorado!). And Rockport has all the services/stores you need plus a shrimp fishing fleet, an oyster fleet, and charter fishing in the bay and Gulf, so lots of great seafood.
Beautiful sunsets, lots of water and shore birds (including whooping cranes right in town during the winter), and a long, lighted fishing pier make it hard to leave Goose Island!