Check out:
Central Ohio Airgunners
Wyandot County Airgunners
Airguns at Fairfield Sportsman's Association
Sherwood Airgunners of Steubenville
Northeast Ohio Airgunners
These clubs host AAFTA style field target matches & benchrest matches. From April through October, one or more matches nearly every weekend. Some of them host indoor benchrest through the winter months.
NOA & FSA have websites, not sure about the others.
Airgunning is thriving in the Buckeye state.