Nobody mentions that both Pigeon Forge and Gatlinburg are ON THE EDGE of Smokey Mountain National Park! I've been probably 5 or 6 times, and the park is absolutely the best part of the area. There is a cool visitor center, lots of hikes to do both easy and tough, long and short - lots of waterfalls to see, creeks to play in, old structures/homesteads to tour (google Cades Cove). Kids would love it for sure. If they get tired of outdoorsy stuff Pigeon Forge and Gatlinburg offer the touristy entertainment too.
The park is a great place to have a good camera and tripod too, Tim.
If you do go, do not miss the Roaring Fork Motor Trail, Cades Cove, and Clingman's Dome.