Salt Lake City. I am within a 15 minute drive of more than 8 canyons. Amazing hiking and skiing of course. The religion stuff isn't a a big deal if you live in the city. Some good privates and publics depending on kids age and need. It does get quite warm here in the summer though. And the air quality is awful. Park city may also suit your needs. Smaller city, better schools.

Idaho.

Denver can get hot in the summer and I wouldn't call it a smaller city. They also have the same school issues as many other cities.

Colorado would work. The Denver suburbs have extensive trails, open space, sidewalks, and playgrounds. Skiing is excellent, but traffic to the ski slopes is terrible. The cons are the cost of housing and some people don't care for the arid climate. There are numerous smaller towns west of Denver like Evergreen or Conifer that would have you out of the city but close enough for shopping.

Another thought is upstate NY. You could live in the suburb of a medium sized town like Syracuse. There are even more outdoor activities than Colorado because of the lakes and rivers, but the skiing and climbing pales in comparison. Winters are gray unlike Colorado and property taxes are high because there is a large school tax. The schools are really good. When you pay teachers a good wage, you get quality teachers. PE in one of the school districts includes cross-country skiing and hiking.

Falmouth or Yarmouth, Maine. Great schools, just outside Portland, easy access to tons of outdoor recreation.

Clearly, there are so many and it depends on what people want. Lakes? Rivers? Coast? Warmth? Skiing?

Boulder, CO

Flagstaff, Arizona.

Seattle?

Madison WI. Spent the most delightful summers there as a kid.

Missoula is pretty great. I think Boise might be too.

No question: Anchorage or Juneau Alaska.

Why does every outdoorsy place have to be so cold? brrr

San Luis Obispo. Not that close to skiing, but can't beat the year-round weather, access to hiking, and ocean sports.

Montana

Idaho or Maine.

Maine has wonderful and beautiful small towns surrounded by gorgeous countryside.