If you want to do the city thing both Columbus & Louisville offer a lot to do. If you want to do outdoors, check out Hocking Hills & The Cedar Falls Inn.

another vote for Hocking Hills .. beautiful area

Check out Berea, Kentucky, or Brown County Indiana for shopping. There is also Amish country up in Ohio, northeast of Columbus.

Nashville is a great one nighter. I don't know if Opryland Mills is open again, yet. The Bluebird Cafe is one of the great live music destinations inside a 500 mile radius of Cincinnati. Plenty of fine restaurants. Mammoth Cave possible for a hike on the way to or from.

At the outer edge of a one nighter is Atlanta. Phipps Plaza and Lennox Square are cater-corner for two of the best malls in the eastern U.S. and superb restaurants abound.

Will second Columbus and Nashville, both well worth a visit. I don't think the Opryland complex in the latter is open yet, but there's still plenty enough to do in the city.

Also, consider Chicago, Indianapolis, and Frankfort (KY), this last only an option by car. Sorry to say, Frankfort is (last I checked) the only US state capital city unreachable by bus or train or commercial flight.

anyway, if you like antiquing, there are lots of possibilities. Lebanon, just north of Cincy, is an old old town, lots of antique shops, and the "inn", The Golden Lamb, where George Washington stopped. Nice food. There is Pleasant Hill Kentucky, a beautiful Shaker Village. Lots of outlet shopping all around Cincy. Jungle Jim's for food shopping.
I guess these are more "day trips" from where you are, without an overnight.