Lots of opportunities in the North East. I speak mainly of the 'dacks because it is there I am MOST familiar. If your looking for an area where you can walk out of your tent and just go, without seeing human or posted signs, still with an opportunity to take a mature deer, do some research on the Five Ponds Wilderness Area and St. Regis Canoe Carry Area.
Both are primitive lands, no motor vehicles, no engines { gas or electric }, Thousands upon thousands of wilderness and forests. Both offer a diverse topography, and fairly easy access, and decent hunting, but it isn't for the out of shape.
Be happy to help further if there's an interest.