I've only been to Columbus a couple of times. One of them, I was a groomsman in a wedding at the Franklin Park Observatory at the botanical gardens:
Franklin Park Conservatory - Botanical Gardens Very beautiful and also had a collection of Chihuly glass.
Also, the Ohio State campus is something to behold. There is a reading room on the top floor of the OSU library that is well worth the visit for the views of the campus and surrounding areas and because it is a really nice space.
As a tourist only there for a weekend, these two places remain as fond memories from a fun weekend.