Away from the regular tourist circuit – the Golden Triangle, Kerala and Goa – there's another, less-explored India, with hardly a tour group in sight. To mark this week's visit by Prince Charles, here's where to find it.

Kaziranga

This national park and World Heritage Site is the major tourist draw in Assam, one of the "Seven Sisters", the comparatively little-visited North Eastern States that are linked to the rest of India by a narrow corridor of land. They're bordered by Bhutan, Tibet, Bangladesh and Myanmar, and their atmosphere is as much south-east Asian as Indian, with a generally gentle pace of life.

You approach Kaziranga through a flat, fertile landscape of tea plantations, fields of mustard and sunflowers, and rice paddies edged with palm trees. In the villages, men weave rice baskets as big as igloos and children wave to passing cars and coaches. The park, with its grassland, swamp and forest plains, houses tigers, water buffalo, swamp deer, wild elephants, more than 400 species of birds and – the major attraction – two-thirds of the world's 3,500 one-horned rhinos. These curious creatures look like armour-plating on legs, though they do trot around very daintily.

Elephants in Kaziranga Credit: GETTY

Chettinad

In the Chettinad region of India's far south, ghost villages of mansions – some abandoned, others taking guests – were once the homes of rich merchants and bankers. Experience the slow rhythm of rural life and spend whole mornings at a village market.

Kalimpong

Smaller and less busy than nearby Darjeeling, this Himalayan hill station offers exotic atmosphere (mule trains between Sikkim, Bhutan and Nepal used to call here), fine Buddhist monasteries, stimulating walks and superb sunrise views of Kanchenjunga, the world's third highest mountain.

The Himalayan foothills near Kalimpong Credit: GETTY

Pondicherry

It's in the south of India, but it could be in the South of France: this elegant, laidback seaside town, a former French colony, has its own Arc de Triomphe, Place de la Republique and statue of Joan of Arc. It bristles with boules, baguettes and boulevards and exudes Gallic charm.

Seaside Pondicherry Credit: Sastyphotos.com

Orchha

Long-abandoned as the capital of a medieval dynasty, Orchha, 250 miles south of Delhi, survives as a ruin-strewn village with grand palaces riddled by passages, winding country lanes, a lively market place and starry nights as peaceful as any in India. Orchha means "hidden place".

Stroll a mile or so out of town to the Lakshminarayan Temple, where 19th-century murals trace Orchha's history, with wry cartoons of musket-carrying British soldiers carousing with rajas. Nose around the riverside chhatris, temple-like cenotaphs to local rulers, and in the evening wander through the bazaar, where trinkets twinkle and temple pilgrims play music and sing hymns.

Lakshminarayan Temple Credit: getty

Coorg

Deep in the southern state of Karnataka and feeling pleasantly remote from the mainstream, the Coorg district has been called "India's Garden of Eden". It has wonderful rainforest landscapes with good walking, and its capital, spruce Madikeri, is the epitome of welcoming small-town India.

Orissa

The eastern state of Orissa is one of the least visited parts of India. It's a treat for temple-lovers, with 500 in Bhubaneswar alone. Then there's the sacred town of Puri, and the most famous temple of all, the Sun Temple at Konark. When templed out, visit Gopalpur-on-Sea, an unexpected seaside resort.

The Sun Temple at Konark Credit: GETTY

Lucknow

One of the most engaging and bookish of Indian cities, it's famous for its impressive Bara Imambara (assembly hall) and for the Residency, a haunting reminder of the 1857 Indian Mutiny (First Indian War of Independence), where 3,000 Europeans were besieged for five months.

The British Residency at Lucknow Credit: saiko3p - Fotolia

Kumaon

The farms, villages, orchards, haystacks and pine forests of the unspoiled Kumaon Hills, 150 miles north-east of Delhi and bordering Nepal, are a taste of the rural lives still led by the vast majority of Indians. Largely unexplored, it makes exhilarating walking country.

Munnar

Planters literally hung up their hats when they retired in this relaxing lesser-known hill station in Kerala with its tea, coffee and cardamom estates. The hats are still there – 50 of them – in the bar of the venerable High Range Club. Misty hilltops and ridges give the town a faintly Scottish atmosphere.

Munnar landscapes Credit: GETTY

Gujarat

A friendly state that's a quieter alternative to neighbouring Rajasthan. Start in Ahmedabad, with Gandhi's ashram and the fascinating pols (mazes of narrow lanes). Then move on to the Kutch region, with its textile villages and starkly beautiful Ranns (salt marshes).

Kite flying in Ahmedabad Credit: GETTY

How to book

Tour operators recommended by Telegraph Travel include Riviera, Wild Frontiers, Cox & Kings, Kuoni and Audley.