Jaipur & Udaipur — Two Cities by way of Pushkar

Met at Jaipur, a city laid out from nothing in 1727 on a grid by Vidyadhar Bhattacharya for Sawai Jai Singh II — one of the earliest planned cities in India, and painted terracotta pink in 1876 for the Prince of Wales's visit. The afternoon takes the City Palace, still partly the residence of the royal family, and the Jantar Mantar beside it: nineteen masonry astronomical instruments built in the 1730s, of which the largest sundial is accurate to about two seconds. Hawa Mahal's pierced facade is a short walk on.

Amber first, before the heat — the Kachhwaha capital before Jaipur was built, begun in 1592 and grown up the hillside in courtyards of pale sandstone and marble, with the Sheesh Mahal's mirror work in the innermost of them. Jaigarh above it holds the Jaivana, cast in 1720 and among the largest wheeled cannon ever made. The afternoon is the old city: the bazaars inside the grid, Jal Mahal sitting in the Man Sagar lake, and the cenotaphs at Gaitore where the maharajas were cremated.

The long day of the trip, and it is built to be done rather than survived: away from Jaipur by seven, so that Pushkar comes at mid-morning — about three hours — for an hour at the lake with its fifty-two bathing ghats and the Brahma temple, one of very few anywhere, shoes off and cameras away at the water. The dargah of Moinuddin Chishti at Ajmer, fourteen kilometres back, is the most important Sufi shrine in India and is offered on request in place of the fort, not as well as it. Then three and a half hours south to Chittorgarh, the largest fort in India by area, for ninety minutes on the plateau: the Vijay Stambh of 1448, Rana Kumbha's palace and the Kalika Mata temple, with the ruins of three sieges around them. Two hours more into Udaipur by early evening, and down to the ghats for the change of scale.

The City Palace in the morning, the largest palace complex in Rajasthan, built up by successive Mewar rulers from 1559 into a single facade nearly a quarter of a kilometre long above Lake Pichola. The Jagdish temple just outside it dates from 1651. The afternoon takes Saheliyon ki Bari, a garden of fountains and marble pavilions built for a queen's attendants, and the Bagore ki Haveli museum on the ghats. A boat on Pichola at sunset is the thing to do here and is booked on the day at the palace jetty.

The morning is free before the transfer. Options within reach are the Monsoon Palace on the ridge west of the city, which is a twenty-minute climb and gives the whole lake system from above, or the vintage car collection at the Garden Hotel, or simply the old lanes below the palace. Udaipur's airport is about half an hour east of the city, so a midday flight is comfortable and an afternoon one is easy.