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.

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.

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.

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.

Known as both the "Garden City" and "The Silicon Valley of India," Bangalore (officially "Bengaluru") is a techie’s paradise, boasting the highest concentration of IT companies in the country. When you’re done geeking out, there are plenty of gardens, museums, natural features, palaces and temples to fill your dance card. Visit Vidhana Soudha, Cubbon Park and the Ulsoor Lake of Bangalore, well known for its beautiful locales and boating facilities. Bangalore is also a major centre of Indian classical music and dance, and of vivid, cutting-edge nightlife.

Coastal charm meets cultural heritage in the sacred city of Puri, where pilgrims flock annually to celebrate the Ratha Yatra. Besides world-famous temples, Puri boasts beaches and markets that buzz year-round, while the wetland landscape beyond the city retains its wild edge.

The people of Tamil Nadu consider providing food to others a service to humanity. Thus the service in the state capital, Chennai, is first-rate. Treat your senses to some of the richest South Indian flavours in traditional dishes like sambar, rasam, fish curry or kootu. And don't forget to have a cup of full-bodied Tamil coffee, enhanced with chicory—no visit is complete without it.