Minx,
I spent half of last year in Wyoming and have had other shorter spells there in the past few years. I love Wyoming...in my experience, the western/NW side of the state has a higher density of climbing/skiing etc...
As far as lifestyle, if you have a decent job, people seem to live very well. Cody is great. It's about 2 to 3 hours from the tetons and Jackson. Cost of living is higher there. However, close by there are several towns (about 20 min. out) that are not as touristy as Cody and Jackson are. The people in the NW corner are so friendly, but most tend to invest in snowmobiling equipment and not a climbing rack. However, there's fantastic ice climbing just outside Cody in the Southfork Valley with a ton of unnamed/unclimbed ice and alpine routes. I've lived in a few different places and felt that the quality of life was quite good. One other thing, each small town varied quite a lot...Powell where I lived was very stable economically, no polygamy, cows slept safely, but 15 miles east was the next main town where there was a fair amount of redundancy in the gene pool and everyone looked a little too much like their neighbors.
If you find a town that you liked, fit your outdoor requirements, and could keep you employed, I'd say give it a shot. Don't know if you're involved/married, but if not, I found the odds were good there, but the goods were often a bit odd.