I've never been to Knoxville. but if you have a free day in Gatlinburg go over the Smokey to Cherokee NC its a nice drive and takes about an hour, and has a few places to stop and look at the mountains. it has two visitors centers Sugarland's about 5 miles outside Gatlinburg, and Oconaluftee outside of Cherokee. also if your coming from North Carolina into Tennessee there is a exist you can get off to do that if you want it on a travel day, or just go on the parkway.