Keep going east!
If you have the time I highly recommended taking 4 or 5 days to ride the roads between Chattanooga, TN and Asheville, NC. If you want some suggested routes I'd be happy to make a quick googlemap of favorites. The road riding is excellent and the jeep trails are good as well.
To get an idea google Tail of the Dragon, Cherohala Skyway, and Blue Ridge Parkway.
PS - As you get within 50 miles of Nashville watch out for lower speed limits and cops on the Natchez Trace Pkwy. Even on Tuesdays mornings I've found them out and about.