If you want to stay just off I 75, Yarberry Campground Lenoir City, TN is a good option. You'll be 45 minutes or so from the National Park, but assuming you have a toad, it is easy access. If you want to be close to the National Park, Big Meadows or the KOA both in Townsend are good options. There are plenty of other options as well.
Depending on your interests, the Museum of Appalachia in Clinton, TN (just off I75 north of Knoxville) will give you a good taste of life in East TN in the 1800's and early 20th century . Cades Cove in the National Park also has a mountain community that was active when the Park was created in the 30's. There are also several hiking trails - like Abram's Falls - off the Cades Cove loop. There is also no utilities RV park in the Park near Cades Cove. Lived in Knoxville for 15 years and family has roots back to the 1830's in the foothills of east TN.
If you go to the National Park via Townsend, you can travel though the park to Gatlinburg. Shops etc. Plenty of things to see in Knoxville as well.
Jim & Lin