As centrally located as Springdale is then any of those areas Ferret mentioned would work. Huston Woods is north about 25 miles. Just north of Oxford, Ohio (Miami University). You may need a permit to hunt it. Should be free if so. I live very close to it but have never hunted it only rode horses, hike, fish, picnic and target archery there. There are deer but you need to know where the open hunting areas are. A google search ought to help. If the time presents I may be able to show you around and even take the bow on a walk through the woods.
I've heard good things about Caeser's Creek but no first hand knowledge. Peebles, as Ferret pointed out, would be a good area as it is very rural and hilly. Reported to be many deer there. That is a bit east of Cincy but pretty country in my mind.