I grew up going to the Great Smoky Mountains fairly regularly as a kid, my favorite was always to go to Chattanooga. It’s like a mid sized town in the middle of the Smokies, so it’s super easy to drive out into very rural natural areas during the day and drive back to the amenities of town at night. There’s also a lot of fascinating Civil War history in the area if anyone is a history buff.
The aquarium is great, and I’m a sucker for the incline railway and Rock City (featured prominently in American Gods). Rock City is technically in Georgia, but it’s a 15 minute drive away from Chattanooga so it might as well be right there.
If any of the kids are 8 or under they’d probably enjoy the Creative Discovery Museum. It’s a pity caves aren’t an option, because Ruby Falls is an underground waterfall in the area and very beautiful. The other thing we always did was either go horse riding or zip lining.
Oh, and if you see people selling fruit or veg on the side of the road with hand written signs, stop and buy it. It will be some of the best you’ve had. Same rule for boiled peanuts and apple butter.