ShotHotspot has mapped 12 abandoned places in Greene, Ohio, ranked by how often they're photographed, viewed and voted for. The most popular are Graffiti: Beavercreek Ohio, Southwestern Portland Cement and Parts Abandoned Theatre Architecture. Some are private property or unsafe, so get permission before you visit.
We don't know whether you're allowed to visit any of these places. Many are private property, closed to the public or unsafe: get permission from the owner or the relevant authority, and take safety precautions.