In Ohio, if you want to go to an amusement park, there's Cedar Point. Second most roller coasters in one park in the country.
For museums, we have the National Air Museum in Dayton, the largest in the country. It's bigger than the Air and Space museum in D.C. There's also the Cleveland Museum of Art, which is both popular and has free admission.
There's also Playhouse Square in Cleveland with a bunch of theaters, if you want to see a play. Largest theater district outside of New York.
If you want to get drunk after the play, Hofbräuhaus Cleveland is right around the corner.
You can also probably find a firing range somewhere around here. Preferably not immediately after getting drunk.