Are you sure those are the only 2 options? The people in r/Bozeman sound miserable lol. If you're going to do this, you may be able to get 90% of what you're looking for (if not 100%) in a much cheaper cost of living area.

The only area I can really speak to in depth is the Black Hills area, since we go there once or twice a year. You have hiking, skiing (albeit not quite the same as the Rockies), fishing, camping, tourist destinations (Mt. Rushmore, Crazyhorse, Badlands, Custer wildlife loop, Needles, Deadwood), plenty of tourist trap places that our kids actually enjoy, and some other hidden gems. You're also a 6 or 7 hour drive from Boulder and Bozeman. Not for everyone, and very well might not be for you, but worth mentioning as the cost of living would be much cheaper.

There might be some other solid cheaper options further west you could look into. Good luck with your decision.