The holy city of Rishikesh, in the base of the Himalayas, holds deep cultural and spiritual significance for local Hindus. Sacred rivers and mountains set the scene for yoga and reflective hikes, and rafting here is an absolute must. The Beatles got in touch with their Eastern spiritual side here, writing several songs during a 1968 stint at a local ashram.

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.

Udaipur, known as the Venice of the East, boasts several sparkling lakes against a backdrop of the Aravail hills. Jag Niwas and Jag Mandir, islands in Fateh Sagar Lake, are the site of Udaipur Solar Observatory and Nehru Garden. Famous palaces include the magical Lake Palace, now a luxurious five-star hotel, and the massive City Palace on Pichola’s east bank, featuring epic courtyards and stunning paintings.

Matheran is all about the views. Easily accessible via scenic rail from Mumbai, this refuge in the Sahyadri Hills is blissfully free of motor vehicles and affords nearly three dozen lookouts over the Western Ghats and the region's village-dotted plains. Porcupine Point is anything but prickly—rather, it’s an ideal spot for gorgeous sunsets, especially at the aptly named Panorama Point. Avid hikers hit the densely forested and wildlife-rich route to the ruins of Prabalgad Fort.

Lonavala is one of the twin hill stations located near to each other, the other being Khandala. These hill stations are very popular getaway spots for people from Mumbai and Pune, which are very well-linked with Lonavala by road and rail. Monsoons are the best time to visit Lonavala/Khandala.

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.

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.

The city of Mahabaleshwar is a pinnacle of greenery, boasting one of the only evergreen forests in the world. The landscape abounds with lush hills, valleys and lookout points such as Lodwick Point, Arthur's Seat and Babington Point, all of which offer spectacular views. Trot along on horseback for a delightful four-legged tour of the gorgeous Venna Lake area, and savour juicy native strawberries, mulberries and corn.

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.

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.

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.