For us east of the Mississippi, it is pretty hard to beat a DIY hunt in the Rockies for mule deer or elk. I have done several and enjoyed every one.
Overlooked by many, it is also pretty easy, and relatively inexpensive, to have a wilderness adventure in Michigan's UP, northern Minnesota and just across the border in Canada. One of the best trips I have ever done was canoeing in the back country and along the northern shore of Lake Superior in Canada with my bow, a quiver full of judo points and a fishing pole in September. For the price of gas, and small game and fishing licenses it is probably the cheapest way for a mid westerner to experience a true DIY wilderness hunt.
Get a map, pick a spot out and go explore.