Other posts mentioned the good rides, but I'd also add Foothills Parkway and of course Blue Ridge Pkwy if it wasn't already mentioned. You have time to go to
www.madmaps.com and order their map for that area. It is excellent giving you many loop rides that include stops along the way. Each loop ride will give you miles, places to eat and what to see. I'll be there next week for my yearly ride to the Smokies and will be staying in Maggie Valley. If you get to Maggie Valley be sure to see the "Wheels thru time museum".
There is nothing but good rides in the Smokies. A little further south if you have the time visit Helen Georga. It is like an Alpine Village and you'll be there for Octoberfest.