Though it opened to outsiders in 1974, Bhutan, with its pristine landscapes and well-preserved Buddhist temples, didn’t start receiving luxury-seeking travelers until about a decade ago, when high-end hotels started opening in the bigger cities of Paro and Thimphu. A more recent debut is the Gangtey Goenpa Lodge, overlooking the Gangtey Valley. Taking its cue from the 17th-century monastery a quick walk from its front door, the property slips discreetly into its remote hillside location. The floor-to-ceiling windows in the main lounge frame a spectacular vista; soft leathers bring warmth to the 9,000-foot elevation, as do individual fireplaces in the 12 guest rooms. Ask the concierge to arrange a private balloon ride for a bird’s-eye view of the glacial valley. You also don’t want to miss some of the country’s most spectacular landmarks, including the Takstang (Tiger’s Nest) Monastery. Precariously situated on a rock outcropping some 2,600 feet above the Paro Valley, Tiger’s Nest is built around a cave where the Indian guru Rinpoche meditated in the eighth century. Today, visitors reach the monastery after a two-hour climb that is not for the faint of heart.