Your best bet is probably going down the coast (forgetting Chattanooga and Atlanta). Although there are some Southern old towns along I-75, my favorite are along the coast and near I-95 (Charleston, SC; Beaufort, SC; Savannah, GA and St. Augustine, FL).
About ten years ago, we took a road trip through NW Florida from Lake City to Tampa. You'd probably have to start in Jacksonville, but it's only an hour east of Lake City. We took all back roads to the Gulf, then travelled down along the Gulf to St. Petersburg. You can continue om to Sarasota. We stayed overnight in Tarpon Springs which is just north of Tampa. Nice Greek settlement, and it has some of the best Greek food around. Definitely worth a special trip just for the food.
I guess I'd go as far as possible the first day (if you can make it below DC, that would be great), then take your time over the next 3 1/2 days.