An unexpected delight: Discovering stylish Mexico City - the capital Frida Kahlo loved

There is a large queue outside Pujol, one of Mexico City's most fashionable restaurants. But we're in luck: our Mexican friends booked a table weeks ago promising us a big surprise. 

'Just don't expect tortillas or tacos,' they said. 'Or a mariachi band.' They were right. Instead, we sample frogs' legs, larvae and black ants. 

Pujol is just one of the many exciting offerings in the Mexican capital. New hotels and restaurants are springing up all over the place.

The authorities have waged war on traffic and pollution in this vast metropolis of 22 million people. Choked with cars, it was often afflicted by smog, which made breathing difficult and the eyes smart. 

A friend who first visited the city 20 years ago once described it as a wheezing, sclerotic patient. On a recent trip, however, she found life-saving surgery had been performed. 

Now commuters whizz around on the Mexican equivalent of Boris bikes ('Ecobicis') or bendy buses. New underground lines and pedestrian zones have been introduced, trees planted and parks restored.

As our guide tells us: 'Please go back and tell the world the smog has lifted.' Citizens can breathe again - Mexico City has had a makeover. 

The country receives 12 million visitors annually, including 200,000 Britons. And they don't just fly into Mexico City and out again on their way to the beach. Increasing numbers come to explore its historic heart. 

Thanks to Mexican billionaire Carlos Slim, who vies with Bill Gates for the title of richest man in the world, the historic centre has been transformed. Having made his £47 billion fortune from telecoms, Slim has restored heaps of dilapidated buildings and opened his own art collection to the public.

Much of his modern art has travelled to London to be shown at the Royal Academy. The exhibition, Mexico: A Revolution In Art (1910-1940) marks the country's transition from dictatorship to democracy. The arts flourished during the revolution: Diego Rivera, the celebrated muralist, and his wife, the painter Frida Kahlo, established their international reputations in this period. 

Meanwhile artists and writers from all over the world were drawn to the political struggle. D. H. Lawrence visited, as did Malcolm Lowry and Graham Greene. For them, this land of temples and volcanoes, shamans and rainforest, was exotic. One could live modestly and alcohol was cheap. Jazz clubs flourished and Mexico City became a fashionable playground for the avant-garde.

Exploring the city on foot proves an unexpected delight. Stroll down the leafy boulevards of Polanco and Condesa, two of its most elegant districts, and you can easily imagine yourself in Paris or Madrid. Indeed, with more than 150 museums, Mexico City ranks as one of the great art capitals of the world. It may not have a Louvre or a Prado, but it does have world-class collections. 

And there is so much more to Mexican heritage than Montezuma and the bloodthirsty Aztecs. We're staying within walking distance of many museums at the Downtown, one of the city's newest hotels, two blocks from the Zocalo, the main square. 

Once a nobleman's house, the hotel's 17th-century salons have been carved up into elegant bedrooms. There are lively restaurants in its courtyard, a rooftop pool and terrace bar. Our first day proves a perfect combination of sloth and self-improvement. 

We begin with a lazy breakfast of huevos rancheros (eggs and tortillas) before sunning ourselves on the rooftop. After lunch nearby at the Cafe de Tacuba, we stroll to the Palacio de Bellas Artes, the national theatre. Here, Rivera recreated one of his finest murals, Man At The Crossroads. 

In a quiet suburb of the city, Coyoacan, Rivera set up house with Kahlo, moving into La Casa Azul (the Blue House), where she was born and grew up. Keen to learn more about him, we visit one of the country's most popular museums. 

When Rivera, an ardent socialist, learned that Russian communist Leon Trotsky was on the run from Stalin, he invited him to live with them. It is said Trotsky and Kahlo started up an affair.

For Trotsky, however, there could be no safe haven. He moved away from the Riveras, and was murdered by a supporter of Stalin. The house where he met his end is now also a museum. 

We join friends for a road trip. Many Mexicans make the hour or so drive south to the neighbouring city of Cuernavaca - dubbed the Beverly Hills of Mexico City - it's where the wealthy live in grand style. 

En route we hear that the local volcano, Popocatepetl , is unusually active. We are keen to see it, but find roads closed off and nearby villages evacuated. Instead, we check into our hotel, Las Mananitas, and eat dinner on the terrace. 

When our food arrives, we notice our plates have curious dark specks. More black ants? No, a fine layer of ash from Popocatepetl. We can't go to the volcano, but the volcano has come to us.

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