From Cosby, TN take TN rt 339 west (north) about 18 miles. It will dead end into Hwy 411, just east of Sevierville, TN. To get to Cosby, you can explore some of the other routes posted here, such as the Foothills Parkway from I-40 exit (which technically is also TN rt 339 on some maps). https://goo.gl/maps/FEjp48Z5JdJ2
This is a nice mountain valley road. So it follows a creek most of it and in some places there are small properties with pastures for either a few horses or a couple cows. Mostly wooded and meandering
Very good road surface, pavement. Good paint markings. Good drainage. There are the typical occasional few stones kicked up on some right handers where cars run off the road.
While Cosby has some limited amenities (gas station and corner store and a BBQ stand), the other end is near Sevierville with plenty of motels, restaurants, etc.
Motorcycle Road Additional info
I ride this after coming off I-40 from North Carolina. Taking the Foothills off I-40 to Cosby, then this road (339) up to 411, and then come back down 416 to Pittman Center. That completes a very nice scenic way to Gatlinburg, instead of fighting tourist traffic down 321 the whole way.