Re: planning a western deer hunt??
I live and hunt in Washington, but have hunted Wyoming a couple of times. Excellent hunting there, with many mule deer & elk to be found. I've never hunted pronghorn, but there are big herds of them too. Good tags are not all that hard for a non-resident hunter to draw either. I've drawn for elk and for mule deer there, but have also struck out a few times trying for another elk hunt.
One caution on Wyoming - there are areas designated as "wilderness" in which a non-resident hunter must use the services of a guide/outfitter. Still, even with that, there's a large amount of public land avail there to hunt, without employing a guide/outfitter.
Another note - some of the application/draw processes start early. Seems to me that when I was applying for elk tags in Wyoming, I had to have my application submitted in January or February - I know it was very early in the year. The deadline for the deer application was later. If not drawn, Wyoming refunds all but a few dollars. Don't forget the conservation stamp once you're in-state too.
Best of Luck! Guy