I only know of the OBX beach access.
Permit and some rulesI have been told, but did not spend the time to find it in print, "you can take truck with camper on beach, but you are not allowed to camp. you must be in the processes of fishing".
the rules also say "Night driving is allowed on the beach generally from November 16-April 30" I think by night driving, they mean get off at night.
We tend to stay in the national park campgrounds and I flat tow a jeep behind me for driving in the sand.
The national park campgrounds are currently no hookups, but the ones I use have water and dump station available close.
Now I am not 100% sure, but I think I hear up on delmarva peninsula there is a stretch of beach you can camp on.