The best chance you have at getting some good hunting action in is to ask the locals, there is a good amount of public access land that only they know about. Also stay away from the east side of the state, unless you want to hunt shoulder-to-shoulder. I know a few awesome spots that are public access and never get hunted, except for me of course...

The further you go west the less amount of deer, but also a lot less hunters, Plus the deer are just as big. The sandhills(SW) has thousands of acres, but is tough hunting.