There are several opportunities to camp on the beach with nothing but sand between you and the ocean. But it's not an 'alone' experience.
Most hookup campgrounds are separated from the ocean/beach by a small grassy sand dune. But plenty close enough to smell the ocean.
Mustang Island State Park has 50Amp/Water sites with a dump station nearby. Showers and toilet building. It is a parking lot type camping area but a nice small picnic table for each site.
The state park also has a mile and a half for beach open for overnight camping. Can be crowded on weekends. Check with the rangers before driving onto the sand/ beach. I've seen 35 footers down the beach. But not sure I would do it.
Mustang Island SPThere are two county parks with RV facilities including water and electric hookups on the offshore islands - I.B. Magee Beach Park near the Port Aransas channel (north end of Mustang Island) and Padre Balli Park right at the edge of the Padre Island National Seashore. When I was last there in October - I found Magee better, but Padre Balli has a better location -
Nueces County Beach ParksThe City of Port Aransas allows RVs to stay 3 nights on the beach - must have the county $12 parking sticker -
Port Aransas Beach InfoPadre Island National Seashore has one organized campground - nice - but no hookups - cold water rinse showers - Malaquite Campground - $8 per night -
MalaquiteThere is also camping at several other locations - including 65 miles of beach - though you must have a 4WD to go past the 5 mile marker.
Again - be very careful and check with rangers before going onto the beach with a heavy vehicle - especially an RV.
Towing charges to pull it out could be huge - think a few thousand - if you were to get a heavy RV stuck four miles down the beach.
There are some commercial campgrounds - various review sites will give you information about them. Port Aransas is on the Mustang Island end and the Padre Island end is in the City of Corpus Christi.
Look under those cities - but under Corpus - all the commercial campgrounds are on the mainland side of the bay.
The only commercial park in the area we've stayed was Ransom Road RV Park in Aransas Pass - very nice. Not too distant - but definitely not on the beach. We've been very happy with Mustang Island State Park and will be going back there.