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.

Darjeeling, nestled among rolling mountains, is a perfect destination for outdoor enthusiasts. Popular places to visit include Tiger Hill, Batasia Loop and the War Memorial, and the Himalayan Zoological Park and Snow Leopard Breeding Center. What should you bring home? Tea, tea, and more tea—and beautiful local handicrafts.

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.

The misty hills, lush teakwood and sandalwood forests, and acres of tea and coffee plantations of Kodagu are, in a word, stunning. Also known as Coorg and dubbed "The Scotland of India," Kodagu is a postcard-perfect region of scattered villages and hamlets, which are the epitome of old-world charm. Kodagu is ideal for outdoor activities such as trekking, angling and white-water rafting, and major festivals like Keil Poldu (worship of weapons), Cauvery Shankaramana (return of the river goddess) and the Huttari (harvest) festival are a huge draw.