You could run down the nachez trace a couple of hundred miles. It's a limited access, park road with 45 mph speed limit and nice scenery. You can catch it just south of Nashville.
Our group is from the burlington/mississauga area heading south on June 13. Our destination is the southern end of the Blue Ridge Parkway. We're going to take our time riding the 750 km's north. It's a fantastic ride through NC and Virginia. Google it. lots of info available.