Dark clouds were gathering as we left the palace. Running for cover, black-faced monkeys skittered over the rooftops and across the ochre walls, which glowed magnificently under the brooding sky. The first few raindrops were falling by the time we passed one of the palace elephants further along the road. Through a steamy haze we gazed back at it and up to the ridge where the silhouette of crenellations and domed pavilions seemed to take on surreal dimensions. I'd visited the Amber Palace several times before but never during the monsoon – and never with quite such accompanying drama.
I was on a trip around the Golden Triangle, the three-city tour that takes in India's most iconic sights. The circuit from Delhi to Jaipur (with the Amber Palace about 10km to the north), and Agra – complete with the Taj Mahal – is deemed the classic introduction to the subcontinent. Yet the prodigious footfall (more than 1.5m people a year according to 2011 government tourism statistics) includes plenty of visitors on anything from second to seventh-or-more trips. The spectacularly moody weather wasn't the only big change from my previous visits: the great flow of tourists I'd been among had diminished to a trickle.
The last time I'd been at the Amber Palace (late October a few years ago) I'd waited amid hordes for a good half hour in order to ride up the cobbled ramparts to the eastern Sun Gate on elephant back, as the maharajahs did in the 17th and 18th centuries. Yet now in reverse reflex the great grey beasts and their mahouts were queuing up for the tourists.
Did they all get a holiday in low season, I asked as I boarded from a small platform. Not exactly, I was told by the mahout, but the welfare of the 100 or so palace elephants is strictly monitored: from July until October – more or less over the monsoon – the mahouts may take them on just three trips a day up the ramparts, while over the six-month high season they make five circuits.
I was glad to be riding an elephant with lighter duties, but what about the rains – does work stop when it's pouring? "When possible," was the pragmatic reply. However the driver added that in Jaipur the monsoon downpours don't last long and afterwards there's a moment of intense freshness: for desert people it's a jubilant time of year. I felt jubilant at exploring the palace along with just a few groups of (mainly Indian) tourists. There was scope to stand back and take in the views from the public audience hall; to pause for a while in the intricately mirrored chambers of the maharajah; and best of all to wander slowly through the beautiful quarters of his queens.
Thereafter the pink city of Jaipur itself was a joy to amble through. Designed in the early 18th-century on a neat grid system (in accordance with the ancient Hindu treatise Vastu Shastra), the capital of Rajasthan is a place of pleasing proportions – and on previous visits frenetic traffic. While not exactly quiet now, it was considerably calmer. I stopped with ease in the bazaar quarter and gazed at the filigreed façade of the Hawa Mahal – the "Palace of the Winds" from where court ladies looked out on life.
Around the corner I joined a mere gaggle of domestic tourists at Jantar Mantar, the city's extraordinary 18th-century observatory featuring 17 enormous sundials whose planes and curves seem to foreshadow modernist sculpture. Then I browsed the fabulously colourful bazaar stalls: turbans and bridal finery around Badi Chaupar; leather shoes around Ramganj; sweets and spices on Tripolia Bazaar.
From street scenes to sybaritic splendour: I was staying at top-of-the-range Oberoi hotels. And here's another huge advantage of monsoon travel – many of India's most glamorous resorts become more affordable. Summer prices, for example, at Oberoi Rajvilas outside Jaipur and at Oberoi Amarvilas in Agra start at less than half the rack rate (from about £452 per night for a double down to around £205 – still a pricey treat but then these ultra-luxury resorts are the equivalent of Gleneagles).
I felt like a latter-day maharajah at Rajvilas – which is exactly the intention. The main part of the hotel resembles a traditional Rajasthani fort. I was proudly told that it was modelled on nearby Naila Fort, which is privately owned by the group chairman, Mr P R S Oberoi, and at which guests can picnic as part of a special elephant-back excursion. Meanwhile the grounds are remarkable: the accommodation, in neat villas or safari-style tents made with hand-embroidered fabric, is spread over 13 hectares which are home to a 280-year-old temple, a dreamy swimming pool and spa, numerous striking jacaranda and flame trees – and a good dozen show-off peacocks.
Until recently this haven was a world apart, set the other side of the Jhalana hills from Jaipur and reached on a slow and winding road. But the opening of the Ghat Ki Guni tunnel earlier this year has revolutionised access.
In any event, road travel in India is changing fast. Not long ago the drive from Jaipur to Agra was an experience of potholed discomfort uplifted by vignettes of camel caravans. Today there's a smooth highway, albeit still subject to the occasional animal crossing.
It now takes about four hours to reach the former capital of the great Mughal emperors – although you'll probably want to break your journey at the stupendous 16th-century ghost city of Fatehpur Sikri just the other side of the Rajasthan-Uttar Pradesh border. Arriving in Agra, I made straight for my hotel. Not that I was shunning the city itself – I was in quest of what are possibly the best views in all of India: the Oberoi Amarvilas offers a superlative outlook over to the Taj Mahal. Each of its 102 rooms face the 17th-century marble mausoleum, just 600 metres away. From my balcony I intermittently spent a few hours gazing at the world's most romantic monument – glowing in overcast afternoon sunshine; in an evening haze; in the pink of dawn.
Of course, you need to make close-up visits too. Cars are not allowed within a 500m radius, so you walk or take or take an electric buggy to the complex. Visiting at sundown on my first day in Agra was an unexpectedly halcyon event. On previous trips the crush of people gathering here at about 5.30pm had been almost overwhelming. Yet now there were no queues to get in. My fellow tourists were principally cheerful Indian families, strolling by the central fountains, posing for photographs and marvelling at the inlay work of the marble tomb.
Monsoon in Agra for the most part means terrifically cloudy mornings building up to a sharp downpour – the Taj Mahal looks spectacular in such rain – after which the air clears, the temperature drops and there's an almost mystical quality of light.
It's a mesmerising time to enjoy the finery of the Mughals. Not only that of Shah Jahan mourning his favourite wife Mumtaz with the construction of the Taj, but also of queen Nur Jahan, who controlled much of India in the mid-17th century and who built the lovely tomb of Itmad ud Daulah for her father. And then there's the amazing legacy of the great 16th-century emperor, Akbar, which includes Agra's Fort and his serene mausoleum just outside town at Sikandra.
Morning rains were starting as we left Agra for Delhi. Thanks to the Yamuna Expressway, which formally opened in August last year, the road trip to India's capital now takes about three hours. Here the Mughal Red Fort; 16th-century Humayan's tomb (precursor to the Taj Mahal) and tranquil, chipmunk-roamed Lodhi Gardens awaited in joyful, rainwashed glory.
Harriet O'Brien travelled to India with Jet Airways (0808 101 1199; jetairways.com) which flies daily from Heathrow to Delhi. Flights to Delhi are available from Manchester and Birmingham via Brussels. Delhi is also served from Heathrow by BA, Virgin Atlantic and Air India.
Jetair Tours (00 91 11 4323 4406; jetairtoursindia.com) offers week-long tours of the Golden Triangle from £192pp, including car and driver. Accommodation is not included but can be arranged.
The writer was the guest of Oberoi Hotels (oberoihotels.com): the rack rate for a double room per night in The Oberoi Rajvilas (00 91 141 268 0101) at Jaipur and The Oberoi Amarvilas (00 91 562 2231515) in Agra starts at £452 but summer rates fall to £205.
British passport-holders require a visa. India Tourist Board: 020-7437 3677; incredibleindia.org.