San Antonio is my favoriteplace to visit in Texas, been there at least a couple dozen times since 1980. Probably visited Houston more often, but that was usually business.
When I take the RV, I like to stay at Traveler's World for easy access to mass transit. This is not a campground, it is a RV park. Most of the places near San Antonio where you can stay with a RV are RV parks or RV resorts, rather than campgrounds, and most will not allow camping, require you to bring and stay in a self contained RV.
Nearest campgrounds I know of will be north of San Antonio, on the Guadalupe River (a state park) or around Canyon Lake (CoE campgrounds).
Other places I like in Texas:
Davis Mountains State Park
Copper Breaks State Park
Palo Duro Canyon State Park
Goliad State Park
Dinosaur Valley State Park
Fredericksburg at Christmas
Palestine (one end of the railway trail)
Port Aransas and Mustang Island, where there is a state park on the beach, but some of the RV resorts are nicer, if you can get a space.
Tom Test
Itasca Spirit 29B