Land of Mermaids. Land of Orange and Lemon Groves. Land of Colors. This small city in Campania has earned a plethora of alluring names. Famed for its sea cliffs, the town's steep slopes look out over azure waters to Ischia, Capri and the Bay of Naples. The birthplace of Limoncello liqueur offers some good diving, great sea fishing, boat cruises and appetizing restaurants. Excellent hiking trails cross the peninsula. Rent a car or take a taxi if the steep streets look too intimidating.

Once a vital part of a mighty sea power, Positano is today a sophisticated resort on the central Amalfi Coast. Moorish-style architecture rises up steep slopes that gaze out on the Sirenuse Islands. Smart boutiques, selling fashions for visitors to display on Grand Beach, abound in the village. And it’s a great base for exploring the area—you can easily travel by boat to Capri, Ischia and the Grotta dello Smeraldo cave.

It’s nicknamed the Eternal City for a reason. In Rome, you can drink from a street fountain fed by an ancient aqueduct. Or see the same profile on a statue in the Capitoline Museum and the guy making your cappuccino. (Which, of course, you know never to order after 11 am.) Rome is also a city of contrasts—what other place on earth could be home to both the Vatican and La Dolce Vita?

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.

Everyone who visits Paris for the first time probably has the same punchlist of major attractions to hit: The Louvre, Notre Dame, The Eiffel Tower, etc. Just make sure you leave some time to wander the city’s grand boulevards and eat in as many cafes, bistros and brasseries as possible. And don’t forget the shopping—whether your tastes run to Louis Vuitton or Les Puces (the flea market), you can find it here.

In progressive Berlin, the old buildings of Mitte gracefully coexist with the modern Reichstag. Don't miss top historic sights like the Berlin Wall, Checkpoint Charlie, the Brandenburg Gate and Potsdamer Platz. The city's great zoo makes for a fun break from touring the staider attractions.

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 medieval city of Norrkoping is nicknamed “The Manchester of Sweden” because of its historical role in the paper and textile industries. Those industries were powered by the Motala river, which runs through the city. Visit the Himmelstalundsvägen to see ancient rock carvings that date to the Nordic Bronze Age, or explore the Industrial Landscape to get an understanding of what shaped modern day Norrkoping.

Edinburgh is Scotland’s capital city, renowned for its heritage, culture and festivals. Take a long walk around the centre to explore the World Heritage Sites of the Old Town and New Town, as well as all the area’s museums and galleries. Then stop for a delicious meal made from fresh Scottish produce before heading out to take in one of Edinburgh’s many events — including the famous summer festivals of culture, or the Winter Festivals of music, light and ceilidhs.

Iceland’s biggest city, Reykjavik bears the distinction of being the world’s northernmost capital, and for virtually every Icelandic visitor it serves as a gateway, just to the city itself or to the rugged adventure options beyond. Founded in the country’s southwest at the end of the 18th century, Reykjavik has been Iceland’s cultural hub ever since. These days, that culture includes a hip and internationally recognised music and arts scene, not to mention a notoriously wild nightlife.

Mombasa, with a population of 900,000, is no sleepy seaside village. Its beachfront hotels appeal to travellers in search of sun, sand and surf, while its Arab, Indian and colonial European heritage makes for a wide variety of sights to see. Can't find a taxi? Travel by tuk-tuk, a three-wheeled auto rickshaw.