Sorry, Jess . . . was this the question?
To give you a good answer I need to know where you're planning on staying. In Gatlinburg itself, or in Pigeon Forge or Sevierville?
If you're going to be in Gatlinburg proper, I'd say get off at the . . . oh, let me figure out which one's best. The 407 exit takes you through Sevierville and Pigeon Forge before you get into Gatlinburg, but it's a straight shot with no curvy roads at all.
If you get off at Newport and come down Cosby Highway it's a pretty decent road, and not much traffic. It brings you right into Gatlinburg without having to go through PF and Sevierville.