It is the world’s longest cave system. I live about 8 hours away so it’s not a short trip. I would probably spend time in Nashville on the way there or back. Also will probably do a rafting trip in the NC/TN mountains along the way as well.
Its been years since I was there but yes, its worth seeing. You’ll only get to see a small portion of the huge system. Then again, I really like touring caves.
It’s a cave.
It’s grey.
and it’s boring.
Unless you are really into geology, or spelunking, or whatever it is that makes some people think that caves are interesting.
If that’s you, then I suppose it would be fascinating .
But not for me. : 
My family went to Mammoth Cave last year for spring break. It was definitely worth seeing and there are some nice hikes within the National Park, as well. It was an 8+ hour drive for us, as well. We stayed 4-5 nights near the park and then two nights in Louisville on our way home.
Bowling Green has some interesting things to do, too, like the Corvette Museum, a train museum, and a cute downtown square.
Make sure to visit the memorial to the Bowling Green massacre. I wept.
Its probably impossible to get tickets at this point.
Nashville is good to visit and I say that as a non country music fan.
Went there about ten years ago. I thought it was excellent.
I was going to say the same… visit the Corvette Museum and - if they’re doing it - take a tour of the Corvette assembly plant.
I’ve lived in Ohio my whole life, and visited Nashville for the first time a month ago. (We spent the night in Nashville on our way back from the U.S. Space & Rocket Center in Huntsville, AL.) Broadway in the evening is quiet amazing… one bar after the other, with a band in each. The next day we visited the Musicians Hall of Fame & Museum.
I had fun. We did one of the tours where you crawl through tight places and marvel at the original people who weren’t following a guide but decided to cram themselves into spots that don’t really look like something a human could fit through.
I found Carlsbad Cavern more interesting, but that’d be even further away for you. But yes, it was interesting.
Note that how interesting a cave system is does not depend much on its size, and so there might be other similarly-interesting caves closer to you.
you won’t see many stalactites and stalagmites at Mammoth Cave, but I and my family still found it quite interesting geologically, historically and as an adventure.
there are smaller caves in WV we might visit as well. Those are only about 4 hours away. I live in RTP area of NC. (AKA Raleigh Durham)
I went there last year and a lot of the caves are indeed “dry” without as many features as other caves. As a matter of fact I took the tour named “domes and dripstones” whose name implies a lot of features, and we didn’t even see many features until the last room which was, admittedly, spectacular.
However, on that tour I did see something that a lot of caves have but don’t show up close. To get to the “main” portion of that tour, we walked down more than a hundred feet of stairs that took us right down a sinkhole, which was a tight, vertical shaft where you could see the pathway the water had carved on its way down from many different levels, which was an interesting thing to see in person as opposed to on an interpretive sign.
I went there as an early teen with my parents and loved it. At the time they had like an hour hike or so that took you through some pretty tight spaces but nothing too claustrophobic. But if you go and you find yourself stooping to get through for a bit, don’t stand up quickly when you think you have more room. You might not and those ceilings have zero give.
I went years ago and I think it was worth it. There are also some smaller caves in the area that have more interesting formations. This one in particular was nice: https://crystalonyxcaveky.com/
I’ve been to Mammoth Cave a couple of times, it’s a great National Park Experience. The cave doesn’t have a huge collection of awesome formations of like Carlsbad Caverns but the tours are well worth taking (There are various tours scheduled throughout the day–make sure to check on times and availability when planning your visit) . I stayed at the campground and also one of the cottages in the park, both were really nice, especially waking up in the morning to one of the coolest dawn choruses I’ve experienced.
Crystal Onyx Cave is definitely worth checking out! It has beautiful formations and an interesting history. I got a chance to talk to the folks that run the place while waiting for my tour–really nice people.
I thought it very cool.
Unfortunately, the neighboring “Stations of the Cross Mini Golf” is no more! 
The voice of personal experience?