Wyatt,
You're making me drool. Anywhere I want to hunt? What a thought! Well, it's not going to happen, so I'll just throw out my dream list, and you can take it from there. I'll define great hunting as "having few hunters, lots of elk, and big bulls." All of what I say below refers to public lands. In every state, private ranches add a different dimension, but I've never hunted any private ranches. Maybe I will someday.
Arizona would still be my first pick, partly because I like that flat, blah-looking juniper country. It intrigues me. But the main reason would be plentiful elk and big bulls. Arizona has it. (Well, it has way too many roads and a few too many hunters, but I could deal with that if the ADF&G would send me a tag.) Problem is, Arizona doesn't issue a lot of tags. Nowadays, if you could draw an Arizona archery bull tag every 10 years, you would probably be doing well.
Some of the limited-entry hunts in Colorado have great potential. I'm accumulating preference points with hopes of drawing another good one there.
Right up there would be some units in Wyoming. Many are limited entry and archers are relatively scarce in much of Wyoming. So, if a guy can draw, as a nonresident, he can have some pretty fabulous hunting.
I also like northwestern Montana. It's some of the most awful country I've ever hunted (meaning steep and brushy), but for that reason it has some very good elk. So do the Missouri Breaks, but they also have a lot of hunters, which diminishes its appeal for me.
My home state of Idaho has some very good hunting, and I love it because it's remote. A guy can still find a lonely elk or two in this state. But he'll work for that opportunity. And I'm note sure our elk are doing all that well. In the famous Clearwater drainage, elk numbers are down markedly. And south of the Salmon River, nearly all the way to Boise, it seems like wolves are having a significant impact on some elk herds.
Oregon has some limited-entry units with fabulous elk hunting. A guy just needs to apply religiously to get one of those tags. Utah also has some excellent limited-entry elk hunts. And Nevada may be the best state of all -- if a guy could ever draw a tag, which isn't likely. I suppose some people would have expected me to list New Mexico at or near the top. Certainly it has some great elk hunting, but I think it has some serious elk-management problems these days, and, from what I hear (I haven't hunted there in several years), the quality of bulls has declined in many of the famous big-bull units. Besides, NM is a little too proud of its elk tags. If the state would get back to managing for monster bulls, the tags might be worth the price.
With all of that said, I didn't really answer your question. I guess that's because you really can't pick one state in this day and age, because almost all have restrictions of some kind or another, particularly on nonresidents. So you have to play the system in order to get one of the really good hunts every few years. Then you can fill in with over-the-counter tags on the years you don't draw the blockbusters. I hope this gives you some ideas, or at least something to dream about.
Dwight