This immaculate city sprawls across more than a dozen islands in a Baltic bay. Tour the Gamla Stan, or old town, with its narrow cobblestone streets and buildings that date back to the 17th and 18th centuries. Stop by Stortorget Square and its historic stock exchange, the hall where Nobel Laureates are honored, the great warship Vasa and the Royal Palace to watch the changing of the guard. A trip to Drottningholm Palace, which houses a splendid working 18th-century theater, also is popular.