We took a road trip through Kentucky to see several sites. We've detailed each site more below, but in case you want to follow our itinerary, here's what we did:
Day 1: Took an evening flight to Cincinnati and checked into the airport hotel via their free shuttle. Well, technically this airport is Convington (CVG) which is in Kentucky.
Day 2: Went to the Creation Museum and then checked into our hotel in Cincinnati. We took this opportunity to walk around the city some. The University of Cincinnati has a beautiful campus. Like with many universities, the areas around the university are best visited in the daytime.
Day 3: Drove to the Ark Encounter and then drove on to Frankfort.
Day 4: Toured the Old State Capitol (guided), the current State Capitol (self-guided), and Buffalo Trace Distillery (guided) in Frankfort. Then we drove on to Louisville-ish and checked into our hotel in Clarksville, Indiana, just on the other side of the river.
Day 5: Drove to Mammoth Cave and then back to Lousiville. On the way back, we stopped and did a quick tour of Abraham Lincoln's birthplace.
Day 6: Toured Louisville as we went to the Louisville Slugger Museum, American Printing House for the Blind, and walked around downtown.
Day 7: Explored Clarksville and then took another afternoon flight home out of Louisville (SDH).
Note that this itinerary utilizes two different airports in Kentucky which can increase your flight costs and will most certainly increase your rental car costs. You may find that it is more advantageous to do a little more driving and use the same airport. I believe CVG is the bigger airport, so your best bet is probably just using it if you go the one-airport route.