Little Talbot Island State Park campground, a short walk across A1A from the beach, has 24 RV/tent and 12 tent-only sites, each with 30amp service and fresh water. For the most part, the sites are relatively private located on several loops that meander through a live oak hammock. A beautiful setting for sure, but note: maximum RV length is 30'. Another interesting aspect of this campground is the ability to use trees you hang a hammock, at certain sites, which is unusual because many places don't allow that. The campground has 2 large bath-houses, centrally located for easy access that were kept clean and tidy by the friendly park staff; nothing beats a good hot shower after a day spent hiking, biking, and beaching.
We stayed at site 36 which backs up to the salt marsh, making if one of our favorites; it also is one of the few that would accommodate our Jay Feather 24T. It's also very close to the put in spot for boats and kayaks. Our 4 legged travel companion, Terra, loves going there, but a word of caution: no dogs on the beach. You can, however, drive a few miles north on A1A to some beautiful dog-friendly beaches on Amelia Island.
We stayed for 2 weeks and could have stayed for 2 more, but life calls. We are already planning our next trip in a year because the sites fill up fast. There is a reason for that.