When in Gatlinburg, day hike half way up the Mount LeConte trail to the walk-behind waterfall. It is nice exercise and free.
Townsend, Tennessee near Gatlinburg has a great tubing biz or for free you can just park along the river and swim/wade in the clear mountain stream.
In Nashville, Visit the Belle Meade Mansion and Percy Warner, Park the same day. At Centennial Park go inside the Parthenon to look upon the giant statue of Athena.
At the Vanderbilt campus visit the base relief wood carving of the Last Supper in the Upper Room Chapel.
Nashville - Pancake Pantry for breakfast. Bluebird Cafe in the evening for music (lots of famous musicians have played there), Opry Mills Mall (next to Opryland). My kid is a Vanderbilt graduate, so I’ve been to Nashville quite a bit.
If it’s the same river I went on, I’d recommend against it. The river was shallow that day anyway; there were a lot of rocks in the river to get scratched on and just generally slow you down.