Just in time for lunch on day one you will come upon New Market, VA. Just off I-81 is this wonderful establishment. My most recent visit there in May was most satisfying: http://www.roadfood.com/Restaurant/Overview/427/southern-kitchen
If you start real early, forty or so miles down I-81 is this: http://www.roadfood.com/Restaurant/Overview/504/wrights-dairy-rite
Take the 250 West exit, follow straight for two miles and you will literally run into it at the bottom of the hill entering downtown. If you have some time, take a walking tour of Staunton, "the Queen City of the Shenandoah
". It is a Victorian-era gem.
Those are my last recommendations about places I know well. Others will have to advise about Knoxville, Memphis, and Little Rock - they are "drive-through" cities for me as I split my Dallas - DC drives into Dallas - Nashville and Nashville - DC segments.
Of course a visit to Franklin's BBQ
in Austin is mandatory
. I think it's fair to say that it is now the best-known BBQ place in the free world. There is a national ad running now with Chef Nobu visiting Aaron Franklin!
Get there early; don't make Hitler's mistake!