Try going to the farms in the SPRING.
Ask for permission to hunt groundhogs. You will be welcomed with open arms. Get to know the fine people that own the farms over the summer. Offer to help out around the farm when you're done hunting groundhogs.
Later ask for permission to hunt whitetails and turkeys.

If you give a little, sometimes you get much more than you expected.

Farmers are bombarded with guys that come at the last minute and want to bring a small army with them. If you want to bring a friend, be careful of your choice. Don't EVER litter, cut fences, or take any other liberties, including cutting limbs and tress for shooting lanes without permission.

Lastly, don't forget to go back when the season is over with a nice frozen turkey or a ham. Be sincere and honest with them and you'll never hurt for a place to hunt.

Northern Ohio has urban zones near Cleveland that allow you to shoot does. Within an hours drive your pretty close to a lot of fine public land also. The Grand River Wildlife area has no shortage of deer.

Hope that helps.