I've been just about everywhere in the mountain west, So here's a bit of advise.
Riverside WY IS NOT a mountain town - I'd avoid
Bozeman MT IS expensive (nearly as expensive as Jackson and gets pretty damn cold, I lived there)
Cody WY would be intriguing as long as you can tolerate or even enjoy tourists, and winters aren't too bad.
Missoula would be cool, but if you are looking for a small town, Plains and Hamilton near Missoula would be better, but all get fairly cold and a bit of snow.
Add to the list:
Spearfish, Custer, Hot Springs and Hill City South Dakota (Black Hills - Hot Springs has the best weather). South Dakota has ridiculously cheap housing relative to Montana and Wyoming, but a lot of work is seasonal because of the tourism in the Black Hills (Mt. Rushmore and the caves)
Lander Wyoming - winters are pretty mild, has a 4-year liberal arts catholic college, and the National Outdoor Leadership School, but not a whole lot of single ladies. Pay in Wyoming is considerably higher than it's neighboring states.
There are a few mountain towns in northern Idaho...Moscow and Sand Point come to mind. Moscow I believe has a small college and decent weather, and you're not too far away from the artsy Couer D'Alene.
I'm sure there are a lot of places in Utah, but I'm not terribly familiar.
Silver City New Mexico would be another one to look into. It probably has the best weather.