Padre Island National Seashore (south of Corpus Christi) $14 per night, $7 for seniors,
Mustang Island, Mustang Island State Park, and a bunch of private parks, all on the beach. Use the ferry at Port Arthur to head north-east towards Houston
Matagorda Island - a Lower Colorado River Authority park. exceptionally nice, lots are triple size most places with full hook ups. nice beach and fishing.
If you like the bright lights then Galveston is the place to go, try Jamaica Beach rv park or the City rv park
Recommendation - use google earth to scout out the area.