I think your best bet is the Cow/calf option in Wyoming. Leftover tags are on sale right now, and are very reasonably priced. Go on their website and see what opportunities are available, look at their statistics by hunt and by unit, and find one with a decent percentage of success. You will never find a place with good elk hunting without other hunters, but your best bet is to go a week after the season opens and stay out of the woods on the weekends.