Welcome to the forum.
Unfortunately, there are very few public hunting areas in Ohio where you can avoid other hunters, if any at all. Especially during the rut. But don’t let that discourage you. The majority of those hunters are lazy or tend to overlook high quality ambush spots. My advice to you is find an area near some comfortable accommodations. Then spend your first 2-3 days with your focus on reconnaissance. Hunt, but make it a priority to scout and assess the lay of the land. Key in on acorn flats for your evening hunts. And find funnels, saddles, or scrape lines on secondary ridges (benches) for your morning hunts. Don’t be afraid to get aggressive and hunt close to doe bedding areas. Good luck, enjoy your time here, and above all else be respectful of the land and other hunters.