Las Casitas, A Belmond Hotel

Each of the twenty casitas at this Belmond resort sits on its own acre in the Colca Valley, a canyon country that makes the Grand Canyon feel modest. It's a small-villa luxury experience in the high Andes, with plunge pools, soaking tubs, and underfloor heating keeping things comfortable after a day on horseback. The Michelin Guide awarded it 3 Keys. Getting here takes effort; Arequipa is a hundred miles away, which is rather the point.