Depending on how you route yourselves, a little gem I discovered riding back from Ohio through east TN a few years ago - The Lost Sea in Sweetwater, TN.
It's on TN 68 about 35-40 miles north of Tellico Plains (and just southeast of I-75 between Chattanooga and Knoxville). Not far out of the way if you plan to ride the Cherohala Skyway from near Robbinsville, NC to Tellico Plains, TN.
Largest underground lake in the Western Hemisphere; second largest in the world. It only took me about 2 hours or so to take the tour of the cavern and the pontoon boat ride on the lake and hit the gift shop. Trout as big as my leg in the underground lake, thanks to an old university experiment. A one-of-a-kind stop IMHO.
Open 364 days/year. Closed Christmas.
I found it entirely by accident looking up a red star symbol in my road atlas while planning that trip.