Oh, heck, you're practically in NE Ohio. I dont know that area nearly as well as farther east, but if that's anything like my impression from driving through there a bunch, there's plenty of deer. Plenty of small to mid-size pieces of public as well. My guess is it can get fairly crowded in popular spots, but I'd bet there's some little overlooked places too. Bow will likely offer you better opportunity than gun hunting anyway, plus it can be less obtrusive hunting the fringes of some of those smaller properties and can buy you some access either to hunt or to cross private ground.
My only advice is that a small overlooked piece of land can be as good or better than a bigger piece that gets a lot of pressure. And anywhere in that area save for the really much bigger chunks of land, it's likely that the deer will split their time between the public and adjacent private, so in many cases you may be able to at least partially scout from the road evenings and AM to see where deer are in fields feeding adjacent to public, and target places to check out on foot that way...realizing of course that other people will do the same. I tell people that havent hunted deer before to take any legal deer to get experience under their belts and maximize their opportunity for at least several seasons, so dont get caught up in the "big buck or nothing" stuff that dominates media and hunting forums until you've killed a solid handful of deer--which could take a while. If you have the opportunity, get someone you know who is really into deer hunting to go scout one of those properties with you and help point out what they look for as far as finding food, bedding, trails, and how they would se tup thinking about the wind, terrain and access. Doing that in person with someone who knows what they are doing will cut years off your learning curve, and having a solid dozen+ spots like that under your belt before september 1 would set you up for a great learning season.
Regardless, you could do a lot worse than to start from fields where you've seen deer on or adjacent to public land (or start from any concentration of deer food that has some old tracks and scat or old rubs, such as brushy clear cuts, berry patches, oak flats, isolated white oaks, or even old orchards in the very early part of the season), and check out the adjacent areas. Look for deer trails between the food source and nearby secluded brushy areas or knobs and ridges where deer will be hunkered down during the day, and find terrain features along those trails like little stream gulleys, small marshes, hills, etc that concentrate animal movement between the food and the bedding, and set up 15 yards downwind of the most heavily-used trails. Dont walk through the deers path of travel on the way in when you're hunting, and be there an hour or two before you think a deer will show up--figure they'll be up moving an hour or two before dark, and may not get to the food source until right at dark or even later, and will reverse in the AM. That's a simple recipe to kill a doe in just about any season, do that a bunch of times and sooner or later one will walk by.
Oh, and get yourself a good pair of rubber knee boots and dont let a little water get in your way.