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.

Want a taste of being royal? Eat in Hyderabad, where culinary traditions have been passed down from the Nizam monarchy. Arabic, Turkish and Mughlai influences are easily recognisable. The city is famous for its rich, aromatic biryani made with lamb, chicken or vegetables and served with fragrant basmati rice. Satisfy your sweet tooth with double-ka-meetha, a bread pudding.

East meets West in this sun-soaked state, where Indian culture intertwines with Portuguese influences left over from a 500-year occupation. The beaches have long served as a magnet for serene hedonists. To the north, the tourist-centric scene is prevalent, with an international flair that is now skewing more hip than hippie. Travel south for stretches of unspoiled sand and an escape from large resorts. Temples, mosques and wildlife sanctuaries provide diversions from the beach.

The kings of the Wodeyar dynasty set the bar high for the southern cultural capital of Mysore. Ornate palaces and the Gothic St. Philomena's Church with its 175-foot spires pack a visual punch; local institutions keep Carnatic classical music and dance in the public eye. A prominent 11th-century temple sits atop 1,000 steps on the city's outskirts. Dress to the nines and party like a rock star in celebration of Mysore heritage during the lively Dussehra festival, held for 10 days in October/November.

Popularly referred to as Ooty, this gem among southern hill resorts is covered in eucalyptus and pine trees and coffee and tea plantations. On a clear day, it's possible to see as far as the Mysore plateau from Dodabetta Peak, the district's most prominent viewpoint. The Stone House, a landmark 1822 bungalow, and St. Stephen's Church are remnants of the area's first British settlement. Also noteworthy: formal botanical gardens, a children's mini-garden and a contemporary art collection.

Blossoming bougainvilleas, crumbling cathedrals on leafy boulevards and 18th-century colonial buildings colour the former French colony of Pondy, which sits on the Bay of Bengal. But it's also unmistakably Indian, with colourful festivals throughout the year, several mosques and the Sri Aurobindo Ashram. Quiet beaches stretch north and south from town, good for swimming and sunrise strolls. Pondy is a popular weekend getaway destination from Chennai and is easy to navigate on foot or by bicycle.

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.

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.