Unassuming Brussels is the capital of Belgium, Flanders and Europe. Medieval Grand-Place is indeed grand, with many 17th-century buildings and daily flower markets. Reopened in 2006, the Atomium, Brussels' Eiffel Tower, provides great views, both inside and out. Architecture fans should visit the Musée Horta, home of Belgian master architect Victor Horta. St Gery's clubs and bars are packed all year round. Seafood eateries abound in Ste Catherine. Exploring the narrow streets on foot is more fun than getting snarled up in traffic.

From Shoreditch’s swaggering style to Camden’s punky vibe and chic Portobello Road, London is many worlds in one. The city’s energy means that no two days are the same. Explore royal or historic sites, tick off landmarks from your bucket list, eat and drink in exclusive Michelin-starred restaurants, enjoy a pint in a traditional pub, or get lost down winding cobbled streets and see what you stumble across – when it comes to London, the possibilities are endless.

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

History lovers should know that Milan is not all about trendy shops and designer clothes. Among the city's many historical attractions are La Scala Opera, the Milan Cathedral, the National Museum of Science and Technology and Santa Maria della Grazie, the church that preserves da Vinci's "Last Supper".

Over 15 million gallons of water bubble daily into Budapest's 118 springs and boreholes. The city of spas offers an astounding array of baths, from the sparkling Gellert Baths to the vast 1913 neo-baroque Szechenyi Spa to Rudas Spa, a dramatic 16th-century Turkish pool with original Ottoman architecture. The "Queen of the Danube" is also steeped in history, culture and natural beauty. Get your camera ready for the Roman ruins of the Aquincum Museum, Heroes' Square and Statue Park, and the 300-foot dome of St. Stephen's Basilica.

Originally founded as a Roman city and now home to three UNESCO World Heritage Sites, Seville is bursting with antique charm. The Alcazar palace complex is a stunning collage of architectural styles, and the Cathedral will impress you with its beauty and its status as the burial site of Christopher Columbus. The Metropol Parasol is the world’s largest wooden structure, a massive mix of grids and swirls that contains a market and a terrace observatory.

Over the centuries, many cultures have added their mark to this prized piece of land. Today, you can experience those influences firsthand by exploring Istanbul’s mahalles (neighbourhoods). From the holy sites of Sultanahmet and the 19th-century European elegance of Beyoğlu to the high fashion of Nişantaşı, the vibrant café society of Kadıköy and the football-loving streets of Beşiktaş, it’s easy to see why travellers say that Istanbul isn’t just one city, but many cities within one.

Lying in south central Turkey, the moonscaped region of Cappadocia, southeast of Ankara, is most famous for unique geological features called fairy chimneys. The large, cone-like formations were created over time by erosion of the relatively soft volcanic ash around them. Past cultures have dug into them to create dwellings, castles (like Uchisar) and even entire underground cities like Kaymakli and Derinkuyu, used as hiding places by early Christians. Nearby Kayseri is the gateway to the area.