If you're not homophobic you could spend days or weeks in Columbus. It's not your stereotypical 'redneck' town in the Mid-West and has a lot of cultural things to do.
One of my favorites was the area called Short North - an artsy district with lots of street art, galleries and restaurants. Or for a bit of historic culture head south of Downtown and visit the German Village. The architecture, gardens and parks are fantastic and the whole are id pedestrian friendly. From memory you can pick up a map of the area and take yourself on a self-guided walk. But if it's sport you're after then it's best to head to the north end of town where the stadiums are located. Here you'll be able to catch a game of ice hockey, baseball of American football. about 10 years ago
Visit the campus of The Ohio State University. A great art museum stands at the entrance at 15th Avenue. I second German Village. And the COSI, the Center of Science and Industry, offers a first rate interactive science museum. Look for the Scioto River (pronounced Sigh-Oh-toe--or Sigh-Oh-tah in Ohio-ese) and follow along to some picnic spots on the way to the zoo. about 10 years ago