Don't know how far into the state you want to travel, but we liked Tanglewood Forsyth County park in Clemmons, NC near Winston Salem. Nice trees, reasonable rates, full hookups. Lots to do. Near shops, restaurants.
Also near Asheville the KOA West in Candler seems to be the better of the KOA's. Another option. Mama Gertie's Hideaway in Swannanoa. Beautifully landscaped, clean, quiet campground with great managers. On the side of a mountain but sites are very level. Only negative is for us flatlanders it was difficult to go for a long walk and the restrooms are at the bottom of the hill. No problem for us as we used our own showers. Very convenient area.
