I don't know about on Beech itself, but there's a campground in Foscoe (on Hwy 105 between Boone and Banner Elk) that takes RVs, I think. It's near the turnoff to Seven Devils/Hawksnest. Try googling Grandfather Campground. Elevation would be approx 3,500. We live about a mile up the road and we're at 3,700+.
I've never driven an RV, but I'd imagine the climb up Beech Mtn would put some serious strain on the motor.