Most of the western states probably have what you are looking for. The only one I have personal experience with is Montana. I went on a combination Elk and Deer hunt. You could take either a whitetail deer or a mulie (I took a nice mulie), which was a cool option to have. I know Montana has a large predator population, as well as pronghorn, black bear, waterfowl and upland birds. These types of hunts are usually pretty expensive, my out of state tag was like $800 bucks. Also the best times to hunt these different types of game don't always line up, for example in montana the best time to hunt elk (in my opinion) is during the bugling season in september, and the rut for deer usually takes place in mid to late november. Its beautiful country out there, I would definately recommend it