Carved into the rock face, with fanciful chimneys, cupolas, lookouts and twisting staircases, this gallery, restaurant and bar with a New Mexico–meets-Morocco look is wrapped in legend. What is certain is that it was designed by César Manrique and prominent architect Jesús Soto, and briefly lived in by Omar Sharif (who lost it in a spectacularly unsuccessful game of bridge). Just 2km south of Teguise, it's hugely underrated and blissfully uncrowded, with regular exhibitions and a small museum.
If you arrive in the evening for dinner or a cocktail, you'll really get a feel for the wild celebrity parties that must have once taken place on the edge of sleepy Nazaret (and there's no entrance fee!). Also here are a couple of creative apartments (per week €840).