Rome wasn't built in a day--and you'll need much more than a day to take in this timeless city. The city is a real-life collage of piazzas, open-air markets, and astonishing historic sites. Toss a coin into the Trevi Fountain, contemplate the Colosseum and the Pantheon, and sample a perfect espresso or gelato before spending an afternoon shopping at the Campo de’Fiori or Via Veneto. Enjoy some of the most memorable meals of your life here, too, from fresh pasta to succulent fried artichokes or a tender oxtail stew.

So many of Madrid’s buildings look like castles, you’ll think you’ve stumbled into a fairytale. Even City Hall is astounding, with its white pinnacles and neo-Gothic features. A self-guided architecture tour can begin by the great bear statue in the central Puerta del Sol. Wander by the fanciful Royal Palace before absorbing the natural beauty of Retiro Park, then visit one of the city’s many museums. You could happily cap off each day by nibbling on forkfuls of paella while sipping Spanish rioja.

The largest city in Switzerland is a major contemporary art and shopping destination. Important artworks are displayed in the Kunsthaus and the Rietberg Museum, while those who consider shopping an art can hone their skills along Bahnhofstrasse and Niederdorf. Chagall's stained glass windows in the Fraumunster amaze and Zurich's 500 clubs and bars, including several in swimming pools, pulse with life 'til the early hours. This city on Lake Zurich has excellent public transit and a free bike rental system.