I also recommend that drive on the Blue Ridge Parkway. In the northwestern part of the state, Boone is nice. I live in northeast Tennessee, but only about 40 miles west of the NC state line. Boone is 52 miles southeast of me. Its wild though, because they are like 1700 ft higher in elevation and its like another world up there. Also, just off of the continental divide and heading down into the Piedmont, you may want to check out Mount Airy NC. This is Andy Griffiths home town and where "Aunt Bee" moved to in real life in her later years. Its a quaint little town. Also, going down I-77 just before you get into NC, there is a nice downgrade off of the mountains with a spectacular view! You are in Virginia, but looking off into lower flatland which is North Carolina. On clear days its like you can see for a hundred miles off to the southeast.

The west central part of the state- you can visit the Great Smoky Mountains. Its in both Tennessee and North Carolina. Just off to the west of there in east Tennessee, you have Gatlinburg and Pigeon Forge and is a very large tourist area. Also, in NC, Mount Mitchell is the highest point in the eastern USA east of the Mississippi River. It peaks at 6684 ft. Check out this link.... http://en.wikipedia.org/wiki/Mount_Mitchell

Southwestern North Carolina - Asheville is a neat city and also the Biltmore Estate is there- Ive never been, despite only being 2 hours away, but would like to go someday.
http://en.wikipedia.org/wiki/Biltmore_Estate

Also, just to the southwest of there is Cherokee Indian reservation. There are museums, but I think the big thing there now are the casinos.
Here is a link to their website as well...
http://www.cherokee-nc.com/
the casinos:
http://www.harrahscherokee.com/casinos/harrahs-cherokee/hotel-casino/property-home.shtml

Lastly, if you head just to the south of the North Carolina / Georgia state line is Brasstown Bald, which is the highest mountain in Georgia at nearly 4900 ft.

If you want to hit the big city life and one of the largest cities in the southeast, Charlotte is not too far away.....
http://en.wikipedia.org/wiki/Charlotte,_North_Carolina

Photos I took while in Charlotte in early fall of 2006...



Lastly, some photos I took in late October of last year this was coming out of upstate South Carolina, heading up into North Carolina...
In South Carolina


Crossing into NC



In then into Tennessee.....




and this was on the way to visit relatives in SC. This was I-26 south, just out of TN and in NC.


Hope this helps!