As others have mentioned, the state is large enough to need a couple of moves while you are there. Not knowing specific interest and manner in which you travel I'll throw out a rough itenerary.
Starting from Bristol Tn/Va northbound on I-81.
Along the interstate here you have the Blue Ridge Pkwy running roughly parallel 50 or so miles east. Toad trips up and down the BRP are great, Town of Floyd is an interesting stop for original Bluegrass style music. you could spend maybe 3 days in the area unless hiking is a major interest, then it expands, State parks are great hiking oppurtunities here.
Continuing NE on either the BRP or I-81 a stop near the northern end of the BRP also puts you near Charlottesville and the Thomas Jefferson exhibits. nearby Lexington Va. has the Virginia Horse center, and your fairly close to Natural bridge state park. Again you can easily spend a few days here.
From I-64 here in the Charlottesville area, you could continue on either Skyline Drive through Shenandoah National park or go a little west and take I-81 which is still running parallel to the area from Front Royal Va to Harpers Ferry WV. Through this stretch you will also pass several caverns. From Front Royal I-66 gives a means of getting as close as you can stand to DC. Traffic becomes a nightmare during commuting hours but there are a couple of campgrounds which are close to rail lines which give access to the National Mall, and all the museums. Also Baltimore's inner Harbor is worth a day, the USS Constellation and the aquarium are great visits. You can easily spend a week in this region and have new things to do daily.
From there head back south to Williamsburg Va. The recreated colonial capitol and Jamestown can take 3 days alone, and Richmond and Norfolk are both less than an hour away offering more museums and historical attractions to occupy a few more days.
If you still have a little time, from Williamsburg its about 3 hours south to the Outer Banks of NC. Nags Head, Kitty Hawk, the Wright Brothers Memorial and the perfect chance to try hang gliding from the same dunes where the first plane flew. Several lighthouses in the area and the "Lost Colony" show in Manteo, as well as some beach and fishing time can easily fill any extra days you still had available.
Campgrounds for FHU can be found in other post here, I was just trying to give an overview of possible sights.
Happy motorin