Made of white marble and crowned by a gilded onion dome, the Gurudwara Bangla Sahib and shimmering pool inside it are places of great sanctity for Indian Sikhs, and offer the most atmospheric introduction possible to capital. The complex in its present form dates from the late-18th century and was constructed at a place associated with the eighth Sikh Guru, Guru Har Krishnan, who resided in a bungalow on the spot. At a Langar, or ‘canteen’ in the temple, pilgrims are fed nourishing, free meals of chapatis and black dal by volunteers. If you’re lucky, you may see groups of Akalis, members of a Sikh warrior sect, dressed in traditional ceremonial garb.

Cycle-rickshaws are a relaxing, and eco-friendly, way to explore the lanes of Old Delhi. Different streets are to be given over to different trades in this atmospheric district, which formed the hub of the Mughal city. Dominating its skyline is the massive white dome of the Jama Masjid mosque, the next stop on your tour.

After admiring the view from its minarets, enjoy lunch at one of the famous kebab restaurants below, before driving across the Yamuna River for a taste of modern Hinduism in the form of the vast Akshardam Mandir, officially the world’s largest Hindu temple. Afterwards, visit the ancient Sufi shrine at Nizamuddin, guided by young residents of the local neighbourhood. Clients of a project designed to alleviate poverty in the area, your young guides will enthusiastically show you around the calligraphy shops and perfumeries, and maybe invite you back to their home for tea!

You’ll arrive at Jaipur in time for a leisurely exploration of the bazaar district. The capital abounds with places to sample traditional cuisine, as well as more cosmopolitan fare, and many restaurants lay on folk music and dance as post-prandial entertainment.

Perched on the rim of a dramatic escarpment, Amber Fort retains some of the finest interiors surviving from the 16th and 17th centuries in India, notably a glittering ‘Hall of Mirrors’, or ‘Sheesh Mahal’. Anyone interested in traditional Rajasthani textiles will also enjoy a visit to the Anokhi Museum of Hand Printing, in Amber village. Jaipur itself is a swirl of life and colour, and its numerous monuments and markets provide the focus for the rest of the day. You’ll begin at the famous City Palace complex, which includes the much photographed ‘Hawa Mahal’, or ‘Palace of Winds’, a five-storey façade of elaborately screened windows.

Fatehpur Sikri provides for the focus the morning’s sightseeing. Built at lavish expense at end of the 16th century, Emperor Akbar’s beautiful sandstone palace complex was only occupied for sixteen years, but its buildings remain in fine condition and vividly evoke the opulence of the Mughal era.

Shah Jahan, creator of the Taj Mahal, was imprisoned at the end of his life by his son, Aurangzeb, in Agra Fort, and is believed to have spent the last years of his life gazing at his wife’s tomb from a domed pavilion overlooking the river. On the opposite bank of the Yamuna, the exquisitely decorated Itimad-ud Daulah tomb provides the next stop on your tour. The mausoleum’s inlay work foreshadowed that of the Taj Mahal, which you’ll visit towards the end of the afternoon.

Drive to the train station in the evening to catch an overnight express to Varanasi.

On the banks of the Ganges, Varanasi is among the oldest continuously inhabited places on earth. Hindu pilgrims still come here to bathe in the sacred waters, which are believed to wash away the sins accumulated in a lifetime. After watching worshippers perform rituals on the ghats leading to the water’s edge, you’ll return to Dashashwamedh Ghat to experience Ganga Aarthi, in which teams of young priests in ceremonial dress wave blazing oil lamps next to the Ganges.

Sarnath, just outside the city, was where the Buddha gave his first sermon in 530BC, revealing the ‘Eight-Fold Path’ to his five disciples. The exact spot is marked by the cylindrical Dhamekh Stupa, built in 500 AD on the remnants of a much older one commissioned by the Mauryan Emperor Ashoka.

Sunrise, when the first rays of daylight illuminate the bathing ghats of Varanasi, is the time to take a boat ride on the Ganges. Thousands of worshippers make their way through the pre-dawn darkness to bathe in the river at this auspicious time, and the spectacle when viewed from the water, with warm sunlight accentuating the colours of the bathers’ sarees, is surely one of the most colourful and uplifting in India.

Tucked away in the labyrinth of narrow, twisting streets behind the ghats is a world that would be recognizable to the representatives of the East India Company who came here over two centuries ago. Our preferred walking tour winds up at Bengali Tolla, where several little shrines dedicated to the Mother Goddess, Kali, are still to be found.

A sprawling modern city of nearly a million inhabitants, the Nepali capital can feel overwhelmingly crowded and chaotic on first impressions. But head for its ancient core, where the Shah and Malla kings erected their resplendently gilded stupas, palaces and carved wood pagodas, and things improve dramatically. Durbar Square forms the epicentre of this superbly atmospheric quarter. More than fifty temples, 106 monastery courtyards (bahals) and countless shrines line its narrow, cobbled backstreets. Settle on to one of the terraced platforms of the Manju Devul tower to watch the exotic bustle of marigold sellers, saffron-clad sadhus, stray cows and pigeons.

Patan (aka ‘Lalitpur’ or ‘Manigal’) is the Kathmandu Valley’s second largest town, and boasts an even greater concentration of religious monuments than the capital. Most of them are grouped in the streets around Durbar Square – one of the world’s most beautiful piazzas – where the Royal Palace of the Malla kings houses a wonderful museum dedicated to Nepal’s sacred arts.

Bhaktapur, further down the valley, boasts another impressive concentration of medieval palaces, courtyard monasteries (bahals) and monumental squares – all in high Newari style. Despite being Nepal’s third city, it’s a much more easygoing destination thanks to the absence of traffic from its historic core.

Elephant safaris are the big selling point of the Royal Chitwan National Park. Sitting astride a swaying, soft-footed pachyderm, you’ll stand a much better chance of getting close to the Jurassic-looking rhinos that are the reserve’s big stars, as well as the more elusive tigers inhabiting its core zone. Sightings of Gangetic dolphins and gharial crocs are almost guaranteed, and be sure to visit the critically important breeding centre for vultures, which have declined to the point of extinction over the past fifteen years or so but survive here in healthy numbers.

The one-horned rhinoceros is emblematic of this area, which it shares with a handful of wild (as opposed to domestic) elephants, crocodile, buffalo and bison. Deer such as the spotted and swamp varieties along with sambar are ubiquitous but there are also antelopes, tigers and leopards, hyenas, sloth bears and jackals. A handful of gangetic dolphins survive in the Karnali River and these can be sighted on boat trips.

Pokhara is the only town in Nepal that could be described as a ‘resort’. Lying 198km west of the capital along the Prithvi Highway, it owes its popularity to the magical view of Machapuchare (‘Fish Tail’) reflected in the glassy waters of the adjacent Phewa Tal lake.

You can soak up the famous icy profile in a café on the lakeshore, or from the water on an evening boat cruise. Better still, climb to the Peace Pagoda overlooking the town for a truly jaw-dropping view of the Himalayan giants to the north, which soar from 1000m to 7,500m in less than 30km.