Having lived and hunted in several different states, including IL and NC, I would personally not choose either state to own hunting property. My family operates a big farm in southern IL and we have some excellent deer on the property. Unfortunately, the far northern part of IL ruins the rest of the state. NC has been a very frustrating state for me to hunt in. The dog hunters are known for doing whatever they want and greatly ruin good management.
As stated by others, KS, SD, ND, NE, WY, MT, and OK would be the states that I would look closely at. Good luck in your search.