The city of Istanbul is a vibrant mix of many cultures, due in part to its location (straddling Europe and Asia across the Bosphorus Strait) and, well, in part to its history of getting conquered. The Hagia Sophia, for example, was a church, then a mosque and is now a museum. You'll spot Greek, Roman, Byzantine and Ottoman architecture around town.
Siem Reap, CambodiaMost travelers don't come to Siem Reap because they're dying to explore Siem Reap—they come to Siem Reap because it's the closest city to the amazing Angkor Archaeological Park. And Siem Reap is absolutely fine with that. In fact, it's a bit of a tourism boomtown. You'll find a wide range of hotels, restaurants and nightclubs here, many of them brand-new.
Berlin, GermanyBerlin is a multi-faceted city. So feast your eyes on modern architecture, then visit a Baroque palace. Spend the day at one of the world's finest zoos, then spend the evening listening to one of the world's finest orchestras. Most travelers make a point of taking in more serious WWII-related sights as well. TripAdvisor travelers give high marks to the grim but thorough and thought-provoking Topography of Terror exhibit.
Barcelona, SpainArchitecture buffs should make a beeline for Barcelona. The medieval and Roman buildings in the Gothic Quarter (Barri Gotic) provide quite a contrast to Antoni Gaudi's fanciful architecture, which you'll find all around the city. A visit to his still-unfinished Church of the Sacred Family (Templo Expiatorio de la Sagrada Familia) is a must.