Pettigrew State Park in Creswell, North Carolina has a small primitive (no water, electric, dump and the RV sites are dirt) campground located on Lake Phelps.
It was a warm summer day when we camped here requiring us to run our generator for a bit until the sun got down after dinner. Because there's no electricity offered, I'd recommend camping in the park in cooler months, but there's hiking and swimming in beautiful Lake Phelps. The campground does offer restrooms with showers.
The park is in a relatively remote farming area in eastern North Carolina. We used it as a way point on our way to the Salina on Cape Hatteras.