Mumbai (formerly known as Bombay), India, is famous for its chaotic streets. For bargains and people-watching, outdoor bazaars top the list of attractions. Popular waterfront destinations are Marine Drive, where visitors go to watch the sun set over the Arabian Sea, and the carnival-like Juhu Beach. More sightseeing options are the Gandhi Museum, in the leader's former home, and the cave temples of Elephanta Island. For tranquillity, Mumbai has many religious sites, lakes and parks.

Laid out by British architect Edwin Lutyens, the Indian capital is a striking modern metropolis. A gracious contrast to Old Delhi's winding streets, the grand avenues and stately buildings of New Delhi are rich with history and culture, from Gandhi's Delhi home (and the site of his assassination) to the tomb of Humayun, a complex of Mughal buildings reminiscent of the Taj Mahal. Chaotic traffic is best left to the locals. Negotiate a good price for taxis or travel on the new Delhi Metro.

In Hinduism, Manu was said to have survived a great flood that destroyed the rest of the world. He then recreated mankind in this Kullu Valley town. What a rush, huh? No wonder the towering peaks and verdant terrain of Manali attracts adventure travellers, with heli-skiing, hiking, mountaineering and river rafting the favored active pursuits. Come down from your endorphin high by breathing deeply at the four-story, wooden Hidimba Devi Temple, which sits in the middle of a nearby deciduous forest, or take a medicinal soak in the hot springs burbling from the ground a 30-minute walk from town.

Established in the Himalaya foothills by a British Army officer in 1820, the "Queen of the Hills" stands above the rest with its deep woods, favorable climate and Doon Valley views. Its name is derived from the berry-covered Mansur shrub found in abundance around this trekker-friendly area. Vestiges of its colonial past are still reflected in the cuisine and architecture. For stunning natural sights, head to Gun Hill or Childer's Lodge, the two highest peaks, or the famous Kempty waterfall.

Sprawling tea plantations surround the serene hills of Munnar, which attract adventure travellers hungry for paragliding, treks to Anaimudi (South India's highest peak) and hikes originating at the confluence of three mountain streams. The stone Christ Church, built by the British in 1910, is adorned with renowned works of stained glass, and Eravikulam National Park, about 10 miles away, is home to equally colourful wildlife, including the endangered Nilgiri Tahr (ibex), ruddy mongoose and 120 bird species.

Coveted by empires and republics throughout its history, Innsbruck was the seat of the imperial court of Maximilian I by the end of the 15th century. Trams make getting around the city quick, efficient and cheap. Explore the Tyrolean capital's history at Archduke Ferdinand II's 10th-century Schloss Ambras, the Tyrolean Folk Art Museum, the grand 15th-century Imperial Palace and Maximilian I's famous Golden Roof. One of Europe's most idyllic cities, Innsbruck is nestled in the heart of the Alps.

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.