Far from the madding, sunburned crowds that swamp Ischia, this luxurious getaway sits in splendid isolation on the extreme promontory of Punta Cornacchia. A one-time fortress, now sleekly renovated, it overlooks the blue Bay of San Montano and has nearly everything to tempt its privileged guests to stay put and relax: a glamorous heated pool overlooking a storybook cove; fine restaurants; full spa treatments; plus hundreds of pretty pine and pomegranate trees. Inside, all is white-on-white, accented with antiques and ancestral portraits. Most guest rooms are in the 16th-century Saracen tower. The restaurants—Chandelier (haute cucina, evenings only) and the informal Sciué Sciué—are open to nonguests by reservation.