Certainly the Asheville area is different from the Charlotte/Greensboro area.
In the latter, I would recommend
Tanglewood Park Campground It is located west of Winston-Salem. There is plenty to do in the park
Recreation, including championship golf course, aquatic center, hiking, and much more.
While there the you and the kids would enjoy a visit to
Old Salem, founded in 1766.
About 60 miles away, in Asheboro is
The NC Zoo, the largest walk-through zoo in the world. (The do have trams :))
Tom