You might find Big Bone Lick State Park interesting - there is a fair amount to do there and they have power (30amp) and water. It's closer to Cincinnati than Louisville though, just off I-75.
The Horse Park is big, and close to Lexington, but there is not a lot to do there unless you leave the park or bring your own entertainment. It's a short drive to Lexington and the park is not that far from the highway.
Mammoth Cave is a great park with lots to do (cave tours, hiking, boating, etc.) and has a nice campground, but it's no where near Louisville
If you're willing to go farther South down I-75, Cumberland Falls State Park is also quite nice, with lots of hiking, a couple of fantastic waterfalls, and other nearby things to see and do.
You can get a 50amp hookup there, in some spots...