I'd look at Montana, but check this link for how to get an out of state hunting license, each is differnet and some are damn near impossible (or not worth the effort) to both obtain the license and a tag.
http://www.sportsmanlogue.com/travel...-of-state.html
Again, each state is different, and the other part is checking your style of hunting. For example, Nevada has some great hunting for Elk, but if your not a resident...good luck drawing a tag (they have a lotto/points system) for rifle. But archery or black powder tags can be obtained with less wait/trouble. Good luck!