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.

Srinigar is a modern waterworld, dominated by Dal Lake and its twisting waterways, tree-lined Nagin Lake, and the Jhelum River. Engulf yourself in local culture by embracing your sea legs and renting one of the wooden boats called shikaras for a daytime or twilight cruise. On land, stroll through the terraced hillsides of the 400-year-old Mughal Gardens, created by Emperor Jehangir for his wife, and shop for indigenous crafts like hand-woven silks and embroidered shawls.

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.

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.

Vietnam's bustling largest city sets the cultural and economic pace for the country. The former Saigon boasts charming French colonial architecture and wide boulevards, usually thronged and choked with traffic. Taxis are an option for seeing the sprawling city. The War Remnants Museum shows the Vietnam War through Vietnamese eyes. Don't miss the impressive Jade Emperor Pagoda. Go to the frenetic Ben Thanh Market for food, flowers or frogs. Tour through the Mekong Delta, past rice paddies and houseboats.

Once known for smog, traffic and tacky architecture, Athens is a city reformed thanks to fortunes brought by the 2004 Summer Olympics. Spotless parks and streets, an ultra-modern metro, new motorways, an accessible airport and all signs in perfect English make the city easily negotiable. Meriting more than a stopover en route to the islands, sophisticated Athens sites include many pillars of Western history, from the Acropolis to the Temple of Olympian Zeus, as well as treasures in the National Archaeological Museum.

From Shoreditch’s swaggering style to Camden’s punky vibe and chic Portobello Road, London is many worlds in one. The city’s energy means that no two days are the same. Explore royal or historic sites, tick off landmarks from your bucket list, eat and drink in exclusive Michelin-starred restaurants, enjoy a pint in a traditional pub, or get lost down winding cobbled streets and see what you stumble across – when it comes to London, the possibilities are endless.