Ditto on what Frodo said. Find 129 on your map. You have a white dot on the base of the twisty portion of it on your map above. Basically, all the fun begins at Robbinsville and goes north into Tennessee. I can't tell from the map, but it looks as if you may have chosen it already.
I would suggest you drive up it AND back down it at least once and then take the Cherahola Highway into Tennessee. It has wide sweepers through the Smokey Mountains.
I'm not jealous over the length of your trip in your car, but I sure am jealous over the fact that you're driving these two roads without me on your tail!
I will be vacationing in Robbinsville this year, but sadly, I'll be in our sedan with the wife, dog, and a bunch of crap in the trunk and back seat.
I might still take everything (and everyone) out of the car and make a run up and down the Dragon just for fun!!!