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Yeah, lots to see and do with kids in Appalachia. I used to work at the Lost Sea (a cavern) driving glass-bottom boats in the world's largest known underground lake. It is a pretty good cave tour. Now it is called "Lost Sea Adventure", or something like that. It is better (I think) than Chattanooga's Ruby Falls cavern tour, but Rock City in Chattanooga is okay (for an above-ground scenic view, that is).

The Lost Sea is in Monroe County Tennessee, on Highway 68 between the little towns of Sweetwater and Madisonville, which are half-way between Chattanooga and Knoxville (just off I-75). They have a pioneer village, too (at least they used to). Easy to spend two or three hours there without breaking the bank.

If you and your kids are really adventurous, consider a drive along the Tellico River and jump/dive off of the Baby Falls (a few miles above Tellico Plains in Monroe County and just about a mile above the larger Bald River Falls). It is scenic, even if you don't brave the falls.

Either place (or both) is a good stop between Chattanooga and Gatlinburg/Pigeon Forge (Dollywood) .

Scoop Sea, about an hour and a half away from Biltmore but Chetola resort in Blowing Rock is a relaxing place to visit.

Really want a change of pace, check out John C. Campbell Folk School in Brasstown NC... wife and I went a few years back and it was something I greatly enjoyed. You can either go for week or weekend to scheduled classes and learn folk arts from master craftsman like blacksmithing, carving, weaving, photography, painting, etc... here's a link to their site... just check out the sublinks and you can view class schedules. Plenty of classes geared to guys and the ladies, and Brasstown is a very beautiful area in the NC mountains but about as close as you can get, as it's just north of the Georgia line.
https://www.folkschool.org/

I had done some bowl turning before I went to the school but never any carving so set my sights on the carving class... only went for the weekend and this was the result.

Thanks everyone for the tips/insights, etc. you all have really given us something to work with. For a guy that really didn't want to head to the mountains for vacation (at least during the summer), I'm starting to see the light at the end of the tunnel on this trip. Thanks again for your suggestions, etc. I'll start working up a plan over the next two weeks. If anyone else wants to add their insight, please feel free to do so as well.

Thanks again,

Chris