Mammoth is the first cave I remember visiting as a kid! Take the longest cave tour you think you can handle and enjoy escaping the summer heat. Lush green areas to explore by foot, horse, bike, or kayak. Lots of wildlife like hellbender salamanders, bats, turkeys, and beavers. None of the trails are too difficult but are worth exploring. Nearby towns are pretty charming too.
Within the National Park there are three different campgrounds. Mammoth Cave is the largest, check out the others if you want something more rustic and less crowded. This is a National Park so the facilities are very nice and everything is pretty close (you won't have to move your car during your visit). Lots of shade!