Camping/backpacking Near I-77?

Heading to North Carolina with my wife for some training for her work in mid September.

Her last day's training doesn't end until afternoon, but we would like to make half of the 11 hour drive that day; camp, and wake up and complete the remainder of the drive the following day.

Any suggestions for camping or light backpacking (1-2 mile hike at most) in the general area from Wythville, Va to Charleston, WV along 77?

I did the general "look at Google maps for green spaces", just looking for anyone's more direct experience.

How off 77 are you willing to go. From Wytheville south on US 21 about 15-20 miles to Jefferson National Forest is Hales Lake camp ground, Iron Mountain Trail, etc.

Lots of places you can go call me and I can point you toward what your looking for.
540-239-8326.
Tony