Capri

Capri needs 2 days: the Blue Grotto, a sea cave where light entering underwater tints everything electric blue, on one day, and a stroll through the Piazzetta and the Gardens of Augustus, with views of the Faraglioni -three rock formations rising from the sea-, on the other. May-September is best. It's expensive, one of Italy's priciest islands. It was the personal retreat of Roman Emperor Tiberius, who ruled the empire from there for a decade without returning to Rome, and since the mid-20th century it's become the go-to beach destination for the aristocracy and Italian cinema.