When Dana and Erin Mahoney relocated from Los Angeles to Bozeman, Mont., some 15 years ago, the city, nestled in the Rocky Mountains, didn’t even have a Starbucks.

With three daughters under 6 at the time, Ms. Mahoney left her career in corporate real estate—and the long commute that went with it—in search of what she called a more wholesome environment, where the couple’s children could grow up skiing and shoveling snow.

“I think people at my work and in my life were taking bets that we’d be back within six months,” she said.

More than a decade later, with their youngest daughter going into her senior year in high school and their two older daughters attending, or having recently graduated from, college in North Carolina, the Mahoneys are making plans to move from Montana to the Raleigh area. They have sold their home, a luxury five-bedroom townhouse in downtown Bozeman, for nearly $1.75 million. Their decision to move was partly motivated by a desire to be closer to their children, Ms. Mahoney said, but also because the sleepy city they moved to has become, for better or for worse, almost unrecognizable.

There are now three Starbucks in downtown Bozeman, a Lululemon, and many trendy restaurants and bars. Visitors drive the wrong way down one-way streets Ms. Mahoney said, and revelers post pictures of their flights of beer from local breweries on social media. Some have started jokingly calling the city Boz Angeles—although the population is around just 47,000, according to 2019 figures from the U.S. Census Bureau, up from about 37,000 in 2011.