'The West' is a pretty big area
Yeah, there are a bunch of vast open areas, but there is a bunch of tight timber as well. For the last 20 years I've lived in N. Idaho and around here 150 yards is a long shot. When I lived in western New Mexico there were some shots that were out to 300 yards or so, but to be honest, all the mulies I shot in NM were within about 175 yards or so.
Public land out here can get pretty crowed these days - make no mistake. A hunter can hike way back there for his elk, far from the madding crowd, but he better think about how he's gonna get it out of there.
I am fortunate in that my hunting partner and I have exclusive access to over 600 acres of private land that borders Nat. Forest and timber company land. Lots of animals, but it is thick - t-h-i-c-k.
More and more elk are becoming creatures of the deep woods. You can find them in the nice, scenic open park lands, but after the first few days of the season they mostly hit the timber and stay there.
If you can afford a guided hunt in Wyoming, Colorado, Montana, Idaho or New Mexico power to you. You'll more than likely get into the elk. If you plan a DIY hunt it will be a lot like deer hunting back home - you go to a place where there are hopefully some elk and you hope you find them. Buy a cow call and learn how to use it. Bring the rifle you are comfortable with and can shoot well. Around here the locals shoot elk with everything from .243 and 30-30 all the way up to .375 H&H and .458 Win. They all kill elk, deer, moose and bear.
I must say that during the two years I lived in Pennsylvania I saw more deer and black bears than anywhere else I've lived - which includes Idaho, Oregon, California, Montana, Washington and Montana.