Ohio is great! There are a lot of suggestions in the thread for outdoorsy stuff but if you're looking for city life any of Cleveland, Columbus or Cincy are fantastic (though Cincy would be a little outside your 2 - 4 hours drive time).

Cleveland - art museum is free, they have great breweries and food too

Cincy - American Sign Museum is a MUST see; Cincy Zoo and Botanical Garden is fantastic; Gaslight District is a cool, quieter hip spot; Over the rhine is a cool, but busy neighborhood; Skyline Chili, Graeter's, goetta