I've been meaning to respond to your reqeust for places near the Smokies. Its 100 +/- miles away, but you shouldn't miss the sites around Chattanooga. Chickamauga is a really nice park; obviously a lot of traffic, but its huge and has lots of open space where you will be the only visitor, even in June. The dirve along the top of Missionary Ridge is nice, but of course its right in town, but there are a nubmer of markers. But the don't miss site is Lookout Mountain. The view is spectacular and there are great hiking trails along the edge of the mountain. There's a small NPS center at the top -- the main one is at Chickamauga.

And, on the other side of Knoxville, visit Dandridge. The battle site is not marked, but the town is one of the odlest in the State, and has a three or four block downtown which is well worth a visit. Its still very rural and is close to Gatlinburg.