Nothing says Santorini like an aqua-blue infinity pool, and Katikies has three of them—all the better to take in westward-facing sunset views. Carved out of the cliff side 300 feet above the Aegean, the hotel’s public spaces are connected by a series of bridges and Escher-esque stairways as they descend from the town of Oia above it. Cube-shaped rooms and suites are minimalist but inviting, nearly every surface painted or clothed in calming white; all have verandas, while a few large suites have outdoor plunge pools or Jacuzzi tubs and alfresco seating areas. Upon check-in, guests are given cell phones to summon 24/7 service from anywhere on the property. They use them to order light snacks at the poolside bar and restaurant or make reservations for some of the best sushi on the island at the champagne bar, but the candlelit rooftop restaurant—serving Greek and Anatolian cuisine—is about as romantic as it gets.