You can hunt statewide in Ohio. To hunt on private land, you must obtain written permission from the landowner or you could face a $500 fine. Hunters can hunt on public hunting land controlled by the Division of Wildlife. Certain wildlife areas do require an additional permit to the hunting license required, so check before you step afield. For a map of the Ohio wildlife areas, please visit this website.
Check out these Painesville, OH Hunting resources: