Wow, three days to ride, hmmm……
This time of year I would suggest the mountains for some cooler weather. Although be sure to stop often and keep hydrated. Like Fossil said it will depend on your experience level and desires. But I would think about:
Short answer; north.
Long answer;
Maggie Valley, NC is only 200 miles from Atlanta and a great place to base out of. From here you can get on the Blue Ridge Parkway or many of the other great roads in that area. Head up to Hot Springs, NC for a great ride on Hwy 209; as good as the Dragon for a twisty road without the traffic. One place to check out in Maggie Valley is the Wheels Through Time museum. They have an incredible number of older motorcycles and I highly recommend it.
The Blue Ridge Parkway itself is a great road to ride. That will take you up into Virginia.
Or head up into West Virginia. I highly recommend Hwy 219.
Or all the above: Day one a combination of Interstates and highways up to Wytheville, Va. Day two ride up into Southeast West Virginia and then across into Kentucky, maybe stopping at Pineville for the night. Day three head home via the Cumberland Gap and stay east of Knoxville along the Smoky Mountains.
Try Google Map, type in where you want to go and move the route around to see how different road combinations work for time and distance.