Glamdring,
Colorado has a permit system for sheep and mountain goats, and is open to both residents and non-residents. Basically, you have to apply for three years before you are entered into the drawing. You can hunt either Rocky Mtn Bighorns (a fair amount of permits), or desert bighorns( very few permits). As for mountainous, I've seen goats at almost fourteen thousand feet.
For other game, we've gots lots of elk, mulie and whitetailed deer, antelopes and turkeys. Lots of waterfowl, upland game birds and pheasants on the eastern plains (and in neighboring Nebraska and Kansas). Numerous varmints (coyotes, prarie dogs, etc.) to plink at if you are so inclined. Good fishing for both cold and warm water species, although not in the Alaska league.
As for 2nd amendment friendly, CHLs are at the discretion of the local county sheriff. Some counties issue to all qualified applicants like where I live in El Paso county (Colorado Springs). Some don't issue at all - like in Denver. We do have open carry, and state law lets us carry a gun in our car if we are "traveling", except in Denver of course. And we do have a lot of job opportunities, especially if you are into high tech.
Here is a link to the Division of Wildlife - they have all their game brouchures on-line.
http://www.dnr.state.co.us/wildlife/
Have Fun - JohnDog