I live in East TN too! I'm in Maryville, very close to Knoxville as well as Townsend, Pigeon Forge, and Gatlinburg. For you Tri-Cities folks, my husband is from Jonesborough, and my in-laws still live there.
OP, I don't know how soon you're planning to visit, but we have a very unique experience in the area early each June. At the Elkmont campground in the Great Smoky Mtns. Park, near Gatlinburg, for about a week each June, you can see a wonderous display of nature. Thousand of synchronous fireflies, lighting in unison for a few hours each night. It's the only place in America you can see this. It's amazing! This year's "show" is June 5-12.
If you're looking for something outside of the Great Smoky Mtns./Pigeon Forge/Gatlinburg route, I would recommend Fall Creek Falls in middle TN. We've camped there before and it was great! There are also cabins and a lodge if you don't like to camp. There are great trails, a naturalist who does programs for kids and adults alike, fishing, pedal boats, swimming, etc... It's a great state park.
Chattanooga has a large aquarium, with a salt water side and a fresh water side. The whole downtown area has been revitalized and is very family friendly.
I love Nashville, but agree with a previous poster. The flood damage there was unbelievable and will take months for recovery. My favorite places were the Opryland Hotel and Opry Mills mall -- all flooded.
Hope this helps! Good luck on planning a stay in our great state!