Tanglewood in Clemmons, NC (half an hour west of Greensboro) -- very nice county park a mile or so off I-40. Many of the sites are very unlevel.
The KOA in Greensboro is right beside the interstate. I've never actually been there but if you don't mind traffic noise it would be very convenient.
Hagen Stone -- haven't been there but we have friends who love it.
Oak Hollow in High Point -- very nice, city owned park that would be just a few minutes' detour from your route. Some of the wooded sites are unlevel. There's an open, graveled section with level but a bit narrow sites. The gravel lot is close to the interstate so there's also some traffic noise.