While your in the area be sure and check out Wheels Through Time museum in Maggie Valley NC. Great people and amazing displays of antique motorcycles.

 

You can not go wrong on any ride in the area. Going back in May for a couple weeks. take your pick

 

I would ride the 68 between Tellico Plains and Ducktown. It's a fun one.

 

+1

Agree with everyone else that you need to take at least 2 days if you're going to do the whole parkway. I've done it that way and wished I'd had three days. So many things to see and do along the way. stop at the Pisgah Inn for a bite to eat. Luray Caverns are an awesome site. And stay at the Peaks of Otter lodge right on the parkway. Peaceful and a great buffet on Friday and Saturday nights.

Have fun!