Because the world's biggest city is also one of the wildest, yet simultaneously a place of immense grace and civility. Because summer in the capital is fresher than you would imagine, thanks to the 8,000ft altitude. And mostly because it's so darn cheap to get there.
It might be a long flight, but to compensate, the airport is located close to the city centre. You could get to the heart of the capital for about 10 pence on the Metro, or splash out on a taxi - which will take 10 minutes. The standard conveyance is a Volkswagen Beetle.
GET YOUR BEARINGS
Since the Aztec era, the centre of the capital, and of Mexico, has been the huge Plaza de la Constitucion (1), known by everyone as the Zocalo. During the day, a Mexican flag the size of a tennis-court flies over the square. Just west is the old commercial centre, an area where you can happily spend most of your time. The Zona Rosa ("pink zone") (2) is a couple of miles south west - not especially pleasant miles to walk.
Prices in Mexico are entertainingly low. At the Hotel Habana (3) (Republica de Cuba, 00 52 5 518 1589), a double room costs pounds 10. Even the Gran Hotel Ciudad de Mexico (4) (Calle 16 de Septiembre 82, 00 52 5 510 4040), a paean to Art Nouveau in one of the most stylish locations, costs 1,000 pesos (pounds 70) for a double room, including tax.
British Airways (0345 222111) will get you there four days each week non-stop from Heathrow. Don't buy direct: through discount agents such as Journey Latin America (0181-747 3108) you can travel on this flight for a fare of pounds 468. Cheaper flights will be available from the start of September. Indirect routes - such as Air France via Paris, Iberia via Madrid, KLM via Amsterdam or Continental via Houston or Newark - are slower but possibly cheaper, and allow connections from airports outside the London area.
TAKE A RIDE
Take care out there. After six visits, I am still not confident, when I step on to a bus, that it will go where it is supposed to. Apart from the fast and efficient underground railway, even for the average citizen the public transport "system" is complex and anarchic. And this is what the Foreign Office says about taxis: "Only use taxis from authorised ranks (sitios). Passengers using other taxis in Mexico City face a much greater risk of attack and robbery."
TAKE A HIKE
You could spend all day perambulating around the Zocalo (1) (main square), possibly the greatest public square in the world. Even if you are not staying there (see Beam Down), start gently with a wander around the atrium of the Gran Hotel de la Ciudad de Mexico (4) in the south-west corner. Occupying the north side of the square, the Catedral Metropolitana (5) is a bewildering mix of architectural styles and building work: a repair programme called the Correcion Geometrica is trying to straighten out seismic distortions.
Adjacent, the Templo Mayor (6) was the centre of the Aztec world, and the walk around its ruins gives a strong sense of the pre-Colombian life. The Palacio Nacional (7), another monumental edifice, takes up the eastern face of the Zocalo.
New arrivals can brush up on Mexican history with Diego Rivera's dramatic mural on the development of the nation.
LUNCH ON THE RUN
Vendors of grilled and copiously salted corn cobs will find you before you find them. If you prefer to wind back a century or two, the Bar Opera (8), at number 10, Calle 5 de Mayo, is a sturdy Baroque gem with a good line in lunch. The freedom fighter Pancho Villa was the most celebrated uninvited guest.
Another superlative: the finest museum in all of Latin America is the Anthropology Museum (9) in the Bosque [forest] de Chapultepec. The extraordinary achievements of the pre-Colombian peoples of Mexico are on show, from the art of the Mayans to the science of the Aztecs.
To witness the demographic conclusion of Mexico's history, go back to the centre, wander into the poorer south-east quarter and explore the frantic commerce around the Mercado de la Merced (10), for which the term "bustling street market" seems woefully inadequate. Everything (including life) is cheap in Mexico, but before you decide to withdraw another 1,000 pesos from your cash machine, be warned by the FO that "incidents of short- term opportunistic kidnapping have increased in Mexico City. Victims holding credit or debit cards are required to withdraw funds at a cash point to obtain their release. Travellers should dress down and avoid wearing expensive jewellery or watches. Particular care should be taken when withdrawing money from a cash point."
The 43rd floor of the Torre Latino Americana (11) presides over the city. In return for paying three times the going rate for a beer (ie London prices), you can enjoy smogset over Mexico City. The sun declines through the pollution, bestowing a dull orange glow upon the capital shortly before it disappears behind the mountains ringing the city. As artificial lighting takes over, you can speculate about the stresses of being an air-traffic controller at Mexico City airport, where a phenomenal amount of traffic battles over the single runway.
THE ICING ON THE CAKE
That's icing, not ice-axe. Leon Trotsky's house (17), hard to find in the south of the city at Calle Viena 45. The heavily defended villa remains as it was when the Russian revolutionary was assassinated in 1940. I was shown around by a Leon-lookalike, who even wore the same round glasses. A fascinating, off-the-tourist-trail trip.
A WALK IN THE PARK
The city has a fine pair of lungs: matching Chapultepec, location for the Anthropological Museum, the Alameda (15) is a celebration of life each Sunday afternoon. At the adjacent Museo Mural Diego Rivera (16), the artist's heroic Dream of Sunday Afternoon at the Alameda depicts important figures from Cortes to Rivera himself.
There are branches of Sanborn's, a quasi-American restaurant chain, all over Mexico. But the branch (14) at Avenida Madera 4 is the best in the nation, occupying the extravagant, tile-clad Casa de los Azulejos.
SUNDAY MORNING: GO TO CHURCH
You need walk only a short distance north from the Zocalo along Calle Monte de Piedad to leave the crowds behind and find peace and sanctity at the Santo Domingo church (13), a masterpiece of colonial architecture.
The name of the most intriguing restaurant I found is also its address: Bolivar 12, handily also (12) on the map. Stylish and fun, it serves excellent food and 130 varieties of tequila; in my experience, one brand is more than enough. In the immediate vicinity there are numerous other options.