Organised chaos in Mexico City

It isn't easy to imagine what a city of 20-something million inhabitants would actually look like. In reality, Mexico City is far less crowded and far more organised than you might imagine.

For a start, the city itself (that which lies in the federal district) is neatly sliced into 16 big areas or Delegaciones, which are then subdivided into nearly 1800 neighbourhoods or Colonias. This makes getting around much easier, when you know which Delegacion to scour on a map for the Colonia you're after.

The city has amazing diversity: the inner blocks are neat and tidy and look just like Europe, with beautiful grand tree-lined boulevards and lots of parks. Trendy Roma and Condesa are full of cafes and bars, while the Zona Rosa is the gay capital and its tackiness reminds me a bit of Sydney's Kings Cross.

In between classes we have been checking out different neighbourhoods - we had a great afternoon out in nearby Coyoacan, which is set around a beautiful stone plaza and super-old church, and has lots of trees and stylish-looking villas. We visited the Frida Kahlo museum and then had dinner and drinks at this impressive-looking Cantina, which was decked out with stuffed bulls heads and advertisements for bull fights (common but not massively popular in Mexico anymore).

Move further out and things get a little grimier, with massive busy arterial road networks and entire suburbs of vertical villages - one we almost moved into comprised 50 separate four-storey buildings, with four or five apartments on each floor. And it was one of about 10 such villages on the same avenue.

The federal district is home to a relatively civilised 8 million people, with the remaining bodies spread out in all directions in neighbouring states. Thankfully, the authorities had the foresight to build an underground metro system when it looked like traffic was getting out of hand in the 60s. The metro is a lifesaver - its possible to get from one side of the city to the other in a hour or less, and not have to deal with any traffic.

Another upside to the metro is that it never fails to entertain. A network of buskers, hawkers and beggars are constantly moving through the carriages, selling their wares, playing music through loud speakers in their backpacks or sharing their hard-luck stories.

You have to hand it to the hawkers - normally they are selling everyday items, like batteries, gum and even childrens toys. But each has their own remarkable sales pitch, which they chant as they walk up and down the carriage. The battery guy (speaking in Spanish) - "batteries, get your batteries, only 10 pesos for a four pack. I got AA, AAA. Perfect for your digital camera, your walkman, your torch, only 10 pesos."

The funniest guy was this stout, hairy creature with an enormous 80's style ghetto blaster who was singing along to his favourite hard-rock classics including "born to be wild" on a late-night ride home. And he proved popular - nearly everyone in the carriage gave him some coin after his performance!

The roads themselves are not actually that bad - I was expecting something as mental as Bangkok. Yes, they are always busy and as a pedestrian are really hard to cross - very few pedestrian crossings and nobody indicates when turning. But no worse than some of Sydney's choked arteries in peak hour.

We have been constantly impressed by the ease of getting around the city. Every time we descend into a subterranean metro station the rumble of the next train approaching is never more than three or four minutes away, even at midnight after a night on the town we barely had to wait.

And I know what you (especially if you are a parent) are thinking - what the hell are we doing walking around, let alone taking public transport in Mexico City after dark? I'm not sure precisely where the city earned its dangerous reputation, but in the areas we have been, it is entirely undeserved. I'm not sure where travel writers were staying (maybe they got the wrong town?) but with so many well-lit areas and so many people on the street, the inner suburbs of the city and even where we live near the university feel just as safe as Sydney.

For a start, there are no individuals or gangs of people just hanging out on street corners. Everyone is going somewhere, or doing something. No-one looks even remotely threatening. We felt far more unsafe in downtown Los Angeles walking to the Greyhound bus station past housing tenements than anywhere we have been in Mexico.