There is actually a lot of elevation change in NC, TN, VA and SC.
Many short, 10-mile hikes have ups and downs of 2,500 to 3,500 feet. Those who have never hunted or camped there might be surprised at trails rising 2,500 feet in 3 miles, waterfalls of 300 feet, and the many cliffs and escarpments to navigate.

By the way, I have lived in Colorado, Wyoming and Texas, and run all those mountains, as well as New Mexico, Montana, Idaho while working out there.

Mount Rogers, VA is not far from High Point, NC (which is pretty flat). Go hike it.