Singapore is known as a bustling metropolis that also happens to be one of the cleanest and safest cities of its size in the world. (Just make sure you heed the local laws—something like spitting in the street might merely be considered rude in your hometown, but here, it carries a severe penalty.) You'll find historic sites like the Thian Hock Keng temple, superlative shopping (including gargantuan malls) and numerous beaches.

Tradition collides with pop culture in Tokyo, where you can reverently wander ancient temples before rocking out at a karaoke bar. Wake up before the sun to catch the lively fish auction at the Toyosu Market, then refresh with a walk beneath the cherry blossom trees that line the Sumida River. Spend some time in the beautiful East Gardens of the Imperial Palace, then brush up on your Japanese history at the Edo-Tokyo Museum. Don’t forget to eat as much sushi, udon noodles, and wagashi (Japanese sweets) as your belly can handle.

Bali is a living postcard, an Indonesian paradise that feels like a fantasy. Soak up the sun on a stretch of fine white sand, or commune with the tropical creatures as you dive along coral ridges or the colorful wreck of a WWII war ship. On shore, the lush jungle shelters stone temples and mischievous monkeys. The “artistic capital” of Ubud is the perfect place to see a cultural dance performance, take a batik or silver-smithing workshop, or invigorate your mind and body in a yoga class.

The political, scientific, historical, architectural and business centre of Russia, Moscow displays the country's contrasts at their most extreme. The ancient and modern exist side by side in this city of 10 million. Catch a metro from one of the ornate stations to see Red Square, the Kremlin, the nine domes of St Basil's Cathedral, Lenin's Mausoleum, the KGB Museum and other symbols of Moscow's great and terrible past, then lighten up and go shopping in Boulevard Ring, or people-watch in Pushkin Square.

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".

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.

Lausanne was once an intellectual capital, attracting such great thinkers as Rousseau and Voltaire. Today it is a haven for lovers of water skiing, swimming and sailing. The International Olympic Committee even has its headquarters here. The town's history is evident, though, in its medieval cathedral, the museums of the Palais de Rumine, and Ouchy, the port where Lord Byron wrote "The Prisoner of Chillon" and the Treaty of Lausanne was ratified. For great views, hike up to the Signal de Sauvabelin.