There are lot of parks (called Metro Parks) in Columbus. Some of them are nature preserves, some are picnic areas and a couple are really big with lots of play equipment, trails, shelters... 

The one we found soon after moving here is called Blacklick Metro Park. It's a wonderful park with lots of amenities. We took our chances with the weather and went to explore. Aside from finding lots of "pime combs," it was fun to walk along the trails and enjoy the sunshine.