The caves of Ponza are steeped in mystical mythology—legend has it that Ponza was Homer’s inspiration for the sorceress Circe’s island in The Odyssey. The whole island has a magical feel to it, from the grottoes to the botanical gardens to the underground labyrinth of Roman tunnels. Schedule a boat tour so that you can explore the entire island by sea—a truly spectacular experience.

The valley of Kashmir is as rich with history and political controversy as it is with culture and natural phenomena. Sample exquisitely spiced native cuisines and festive teas, then walk off your meal along the rugged trekking routes to the north. Marvel at the famous houseboats of Srinagar and take a spiritual moment to reflect at one of the many pilgrimage sites and religious shrines that dot the region. Of course, native craftsmanship makes for excellent souvenirs—carpets and textiles are an especial shopping must.

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.

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.

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.

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.

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.

This former British colonial stronghold boasts evidence of over two millennia of habitation, with ornate, architecturally diverse buildings, ranging from crumbing ruins to Victorian treasures. Home to lively festivals and a vibrant artistic community, clamorous markets and packed temples, this city is crowded and polluted, but ultimately invigorating.