Bozeman and Livingston, Montana, have long been known by mountaineers, anglers, and skiers as sought-after vacation destinations. But as these mountain towns have grown, change has brought a plethora of quality dining, art, cultural events, shopping, and music. As a result, it's become an urban experience with a gorgeous backdrop and plenty of options for exploration – in the vast outdoors and tucked within the cozy historic buildings, which makes it a perfect destination for a girl's…