Just outside Funchal, on a clifftop promontory overlooking the Atlantic, the original Cliff Bay is one of Madeira’s most upscale hotels. When the property next door went up for sale, the owners snapped it up, restoring its tiered gardens and a pair of century-old villas — and adding a new wing and a gorgeous infinity pool — to create the even more luxurious Les Suites. While there’s no doubt these, with their ultra-spacious layouts, sea-facing floor-to-ceiling windows, and lavish Greek marble bathrooms, are the more exclusive lodgings, guests will be glad to take advantage of the amenities at the neighboring hotel, including a spa, open-air Jacuzzis, direct access to the ocean, and the two-MICHELIN-Star Il Gallo d’Oro restaurant.