If you like history, the William Howard Taft Presidential Library is very nice and they'll give you a tour of his house, too.
If you go to Newport, Kentucky---which, as someone else has mentioned, is right across the river and has a super-cool aquarium where you can pet sharks and horseshoe crabs (among other things)---you can get one of those Ride The Ducks tours, which will take you through both Newport (which used to be the Las Vegas of the United States before Nevada became a state) and Cincinnati. It's really cool.
If it's open, you could also check out the Reds Hall of Fame. You should also at least drive by Great American Ballpark if you like baseball at all. The smokestacks look really amazing, and you can see the rose garden that is a secret tribute to Pete Rose.