If you drive via Atlanta or Chattanooga (both great cities to visit) your trip will take at least an hour longer. We make the trip from Orlando about 10 times per year. We only use I75 when the roads are closed in N.C. or S.C. as they were during Hurricane Florence. St Augustine and Asheville would both be good stops.
We usually take I-75 going up and I-95 coming back or vice versa. It would be about 9 hours to Atlanta from Miami or you could overnight in Valdosta or Macon. From Atlanta you would then only be about 2.5 to 3 hours from Chattanooga. Check out their forum for things to see & do while there. From Chattanooga head to north and exit at Lenoir and onto Hwy 321, you can then take it thru Townsend with a stop at Cades Cove on the way or stay on Hwy 321 which comes out in Wears Valley.
Coming back I agree with a stop in Asheville, its a good place to visit or Bryson City and explore a bit in that area. Savannah is a must do for us on almost every trip, Gotta get those Pralines on River Street!
Yes I do agree with bornwithwheels he has some great suggestions not one of them could you go wrong by visiting.
Safe and happy travels ..enjoy;)
Jekyll Island, GA is a nice place to stop on the way and you can never go wrong with Savannah. As a FL resident, I think both of these would be great spots because you are going to be approximately splitting the drive in half coming from Miami. On another note, Allegiant Air has great deals from a couple of spots in Florida to Knoxville for very good prices. Knoxville is about a hour away