I'd heartily second the recommendation for Grayson Highlands/Mt. Rogers. There's nothing to compare with unzipping your tent vestibule in the morning and find that you're face to face with a pony!

It really is a pretty place, and unlike a lot of Eastern trails, there are lots of stretches with wide-open views rather than a tunnel of trees. It's also near the Virginia-Tennessee-North Carolina junction, so probably not a hatefully long drive.