want to hunt elk

Your question is so wide open as I can't even answer it. No offense meant. Looks to me that you have A LOT of research in front of you. I'd suggest going to various states' web sites, calling a few of the DOW's and maybe talk to some folks you know who have hunted elk in the past. As the saying goes, if you want to shoot and elk, go to Colorado. Colo has the biggest numbers of all the western states. If you want a trophy, hunt New Mexico, Utah, Arizona or Wyoming. Keep in mind, trophy units tend to take a number of preference points to draw. Each state has a different drawing, different seasons, different everything. You could maybe try a broker for tags but that raises the price. Cabela's has a TAGS program to help non-resident hunters with applications and I believe they charge a fair service fee for this assistance. You basically need to figure out where you want to hunt, then apply. Not an easy process if you've never hunted out west before. Once you decide and apply, if you draw, then you need to get out there and scout prior to hunting. Not speaking for any state other than Colo, non-residents can still purchase bull tags over the counter. However, not all units are open to the OTC tags. A number of units are draw only. Good luck with your research and hope you can get out there in the fall.