Cyprus, a four-hour flight from London, has long been a favorite vacation spot of sun-seeking Europeans. And since the Greek part of the island joined the European Union, a flurry of stylish new hotels have opened. Among them is the recently revamped Almyra. Located in the western port town of Paphos and within walking distance of two of the most revered archaeological sites in the Mediterranean (the 13th-century Castle of Paphos and the intricately tiled House of Dionysus), the 158-room property has a minimalist décor, a slate-lined freshwater swimming pool, and a Mediterranean-Japanese fusion restaurant run by chef Rob Shipman, who was nabbed from London’s Nobu. It’s also a great place for families, proffering bedtime milk and cookies, children’s books in four languages, a dedicated children’s club and swimming pool, and even a selection of organic baby food.