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Rio de Janeiro. Look at any list of the "World's Most Beautiful Cities" and Rio will be on it, usually fighting for the top spot with Paris and Venice. Almost everybody I've met on this trip who's been there has raved about it, in raptures. Expectations are high.

And when it comes to sheer physical beauty, Rio most certainly does live up to all the hype surrounding it. The first thing you notice when arriving in Rio by plane - as I did from Salvador - is the city's breathtaking location, which easily rivals Venice for pure outlandishness. Built on the edge of a large bay, the Baía de Guanabara, along a heavily indented stretch of Brazil's southern Atlantic coast, Rio is wedged against the ocean by mountains dripping with verdant rainforest. Between this backdrop and the sea, the city is dotted with steep granite peaks or morros several hundreds of metres high. While the city's fancy residential and business neighbourhood are awkwardly shoehorned around these rocky towers, its poorer ones - the notorious favelas - cling precariously to their slopes. The scenery is more than a little reminiscent of Thailand's Andaman Sea coast, or Viet Nam's Ha Long Bay - but here there's a giant metropolis built bang in the middle of it. As if this weren't strange enough, a huge lagoon nearly two kilometres across occupies much of the western part of town.

Rio is a city of disconcerting contrasts. Leblon, an über swanky neighbourhood just off Ipanema Beach - one of the world's best-known and most recognisable stretches of sand, perhaps second only to its immediate neighbour Copacabana - can rival New York or Tokyo when it comes to real-estate values. Perched on a morro just beyond Leblon's fancy towers - and arguably enjoying a better beach view than most of that neighbourhood's million-dollar apartments - is the favela of Vidigal. Urban poverty and drug-related violence a stone's throw from Howard Stern and Armani. Boys from the favelas play football on the sands of Ipanema not ten metres from yuppies jogging with their personal trainers.

Cariocas - as residents of Rio de Janeiro are known - are no shrinking violets. They have a reputation throughout Brazil, and the world for that matter, for being loud, brash, hedonistic and appallingly vain. Nowhere is this more apparent than on Rio's legendary beaches. A walk along Ipanema or Copacabana confirms all these points - the last one especially so. Yes, Cariocas love to have fun. As long as the sun is shining, at any time of day they will be on the beach in their hundreds: playing volleyball, football, futevôlei - a typically Brazilian mix of the two - grilling themselves and generally checking each other out. Interestingly, the huge beaches of Ipanema and Copacabana - each is about three kilometres long - are unofficially divided into territories of sorts, with the boundaries between them corresponding to the lifeguard stations or postos distributed at regular intervals. There's the section for retirees, for transvestites (best not to get those two mixed up), for upper-crust Leblon residents, for favela kids. While the beaches of Rio look inclusive at first glance, things might not be quite what they seem...

Unsurprisingly, Rio's beauty is best appreciated from on high; two of the city's most iconic landmarks allow you to do just that. The Pão de Açúcar, or Sugarloaf Mountain, towers almost four hundred metres above Rio's Urca neighbourhood. A two-stage cable-car runs from street level all the way to the top of the morro but it's far more fun (not to mention cheaper!) to do the first section on foot, climbing to the top of the Morro da Urca, the forested sloped of which are crawling with saguis, adorable little marmosets smaller than a domestic cat, frolicking in the vegetation. The cable-car ride to the Pão de Açúcar itself is predictably spectacular, offering jaw-dropping views of Rio, its skycrapers, its morros and its splendid beaches. As far as urban panoramas go the view from the Sugarloaf can't be beaten...except perhaps by that from Corcovado, an even taller hill looming more than seven hundred metres over the city, and visible from almost anywhere in Rio. Due to its extreme steepness the summit of Corcovado - "the Hunchback" - can only be reached by a rack-and-pinion railway from the neighbourhood of Cosme Velho by a circuitous route around the mountain. Even more famous than the mountain itself is what stands on top of it: the 30-metre high statue of Christ, the Cristo Redentor, arms thrown open as if in amazement at the wonder of Rio's beauty below. You can't really help but want to do the same...

There is a lot more to Rio de Janeiro than Ipanema, Copacabana and Christ the Redeemer. Less well known is the city's centro, the beating heart of the modern city where Cariocas work in their hundreds of thousands. It's an intriguing mix of old and new, rich and poor, sparkling and decrepit, refined and grubby. Steel-and-glass skyscrapers housing bank headquarters stand side by side with the skeletons of crumbling, graffitied buildings. The steep, narrow and winding streets of Santa Teresa, an old bairro of old-school bars and samba clubs, are but a five-minute ride from broad avenues filled with honking traffic and besuited businessmen. A weekday tour of the centro - as in most Brazilian cities the business district is not considered safe to visit during the weekend - reveals some wonderful surprises: belle époque cafés made for people-watching, raucous street markets where Christmas trees and decorations are sold under the boiling sun, hulking modernist buildings sidling up to colonial-era gems.

Across Guanabara Bay from Rio lies the city of Niterói, essentially a suburb of its larger neighbour, albeit one with half a million inhabitants. There are two reasons to go to Niterói: the first is the scenic ferry journey across the bay from Rio, a route used by huge numbers of commuters (and consequently nice and cheap) every day. It's certainly a commute with a view, passing right by the runway of the city-centre Santos Dumont airport and offering splendid views of Rio's extraordinary natural beauty - it certainly beats the Northern Line on a Monday morning. The second is the Museu de Arte Contemporânea, a modern art museum perched on a small headland jutting out into the bay back towards Rio. The art - at least as far as I'm concerned - is nothing special, but the museum building most certainly is. Built in 1996, the MAC was designed by the late Brazilian wunderarchitect Oscar Niemeyer: it's a spectacular building, a vast concrete UFO balancing on an improbably narrow pedestal, like something out of Star Wars or Thunderbirds. Far more interesting than the dubious modern art inside are the 360-degree views of Guanabara Bay and its gorgeous beaches. Niemeyer was almost singlehandedly responsible for the design of Brasília, Brazil's modernist capital, built in the late 1950s out of nothing - a place I'd definitely like to see on a future trip to Brazil.

My last day in Rio - my last day in Brazil, in fact - is a long one. Having spent the day covering endless kilometres on foot - exploring the centro, Santa Teresa, admiring an exhibition of Impressionist art at one of the city's excellent cultural centres, catching the ferry to Niterói and back - I collapse back at my hostel and play the waiting game for my early morning flight the next day. Having attempted to sleep in one of the common area hammocks - the flight is so early it wasn't worth booking a bed - I wake up bleary-eyed at 4am and catch my taxi to the airport - the roads are empty and the journey, which can take two hours at peak times, is done in 20 minutes (courtesy of some frighteningly reckless driving, but I'm become inured).

By the end of the day, thanks to the wonder of the jet engine, I'll be over 4,000 kilometres way, back in deepest Patagonia. It's the beginning of the end, but the next few weeks promise to be quite special.

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