Beyoncé and Jay Z called this one. The couple’s 2011 visit to Hvar Island seemed to open the tourist floodgates to Croatia’s Dalmatian Coast. Korcula is Hvar’s more modest neighbor. Much of the island is still untouched: dotted with blue-collar fishing villages and little pebble beaches. Instead of sticking to the Old Town, which claims to be the birthplace of Marco Polo, rent a moped and head west. Travel through olive groves and thick woodlands, and drive off-road to sample Korcula’s signature white wine, Grk, at any number of hopelessly charming family wineries. It’s bitter and earthy — and true to the region’s less fashionable days.