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.

Belgrade's long and storied history is suggested by its architecture, which varies from Byzantine and Ottoman to neoclassic and romantic buildings in the older neighborhoods, and from Art Nouveau to brutalism and neo-Byzantine design in New Belgrade. The city's many theaters, museums, monuments and opera houses boast a deep and fissured cultural life while the beaches and rivers attract sunbathers, sports enthusiasts and partygoers on the popular floating river barges that serve as nightclubs.

Barcelona feels a bit surreal – appropriate, since Salvador Dali spent time here and Spanish Catalan architect Antoni Gaudí designed several of the city’s buildings. Stepping into Gaudí’s Church of the Sacred Family is a bit like falling through the looking glass - a journey that you can continue with a visit to Park Güell. Sip sangria at a sidewalk café in Las Ramblas while watching flamboyant street performers, then create your own moveable feast by floating from tapas bar to tapas bar.