Currently, there are many opportunities for deer hunting at USA Military Bases. The hunts tend to be heavily regulated with many paperwork hoops to jump through, but the patient and determined hunter will be rewarded with amazing hunting grounds. Some bases have more restrictions for civilians than for active duty and retired veterans.
Each Base is like a small state in terms of bureaucracy. Typically the best place to start the search is phoning the MWR Facility. (Morale Welfare Recreation). Other bases have an Outdoor Recreation Office.
Good hunting to you.
TR