3 Best Sights in Capri, Ischia, and Procida, Italy

From the terraces of this beautiful public garden, you can see the village of Marina Piccola below—restaurants, cabanas, and swimming platforms huddle among the shoals—and admire the steep, winding Via Krupp, actually a staircase cut into the rock. Friedrich Krupp, the German arms manufacturer, loved Capri and became one of the island's most generous benefactors.

Two kilometers (1 mile) north of Forio is one of the most famous gardens in Mediterranean Italy, La Mortella. The garden was a labor of love designed in 1956 by the landscape architect Russell Page for Sir William Walton and his Argentine-born wife, Susana. The garden was created within a wide, bowl-shape, rocky valley, originally not much more than a quarry, overlooking the Bay of San Francesco and with spreading views toward Monte Epomeo and Forio. Lady Walton, who passed away in 2010, was a talented gardener in her own right, and first planted the trees of her childhood here (jacaranda, silk trees, erythrina, brugmansia) and then added tree ferns, palm trees, cycads, and rare bromeliads. Native wild plants were encouraged in the upper reaches of the gardens, with dainty vetches and orchids as well as myrtle, from which the garden got its name, La Mortella. Considering the volcanic valley out of which the gardens were sculpted, they are appropriately threaded with pathways of rocks hewn from Vesuvius. In homage to the hot springs of the island, the centerpiece is an elliptical pond with three small islands adorned with the immense boulders that once littered the grounds. Below, underground cisterns were excavated to catch natural drinking water.

Besides some soothing strolls among the well-labeled flower beds and landscaped rock gardens, try to spend some time in the museum dedicated to the life and works of the late English composer, William Walton. The gardens have excellent facilities, with a shop selling Sir William's music, a teahouse for light refreshments, and a theater that hosts a concert series on most weekends; book well in advance for these tickets.

Frustrated by Capri's ongoing commercial overdevelopment, Swedish professor Gunnar Adler-Karlsson acquired the land around the Belvedere di Migliara with the intention of maintaining an ecologically pure area. Covering 11,000 square meters (36,000 square feet), paths lead through rich Mediterranean maquis with more than 60 ceramic panels lining the way with quotes from great thinkers from Aristotle to Einstein. Allegedly the first of its kind in the world, just feet away from one of the most gorgeous views in the world, this park is devoted to peace and reflection. A complete guide, called "Meditation Upon Western Wisdom," is available from the adjacent Da Gelsomino restaurant.