The eccentric Englishman Lord Grimthorpe (who also designed London’s Big Ben) redid this grand villa from the 14th century in 1904. The lavish salons and gardens soon became associated with the 20th-century elite, few more elusive than Greta Garbo, who hid out here in 1937 with her lover, the conductor Leopold Stokowski. The high point of the lavish gardens, quite literally, is the Belvedere Cimbrone, where you’ll have the dizzying sensation of being suspended between sea and sky.