Ten days in Brazil: Rio for the view, Sao Paulo for the food, and Iguacu for the noise

The one everybody has heard of: four kilometres of sand under a wall of hotels, with a promenade of black and white mosaic laid in waves running the length of it. Older and more mixed than the beaches further south, and busy from breakfast onwards. Walk it southwards, towards the point that closes it off.

The beach residents actually choose, divided into numbered posts that each attract a different crowd. Posts 8 and 9 are the busy sociable stretch; walk west towards Leblon for space, past the twin peaks of Dois Irmaos at that end. Swim where other people are, because the shelf is steep and the undertow is real.

The low rocky headland dividing the two beaches, and the best free view in Rio: the whole curve of Ipanema one way, Sugarloaf and Corcovado behind. Locals gather for sunset and applaud when it lands. Arrive forty minutes early for a place on the rock.

The streets a block back from the beach fill from about eight with botequins and small restaurants. No booking needed midweek. Order a caipirinha and something grilled and go to bed early.

A 38 metre statue on a 700 metre granite peak, finished in 1931, with the whole city underneath it. Everyone photographs the statue and then spends much longer looking the other way. Take a layer: it is colder and far windier up there.

A pink mansion against the forest with an Italianate courtyard, a swimming pool and a cafe in it, and rainforest trails from the back gate. One climbs all the way to Corcovado, which is a serious two to three hour ascent rather than a stroll.

Tables in the arcaded courtyard with the mountain filling the gap above the roofline. Busy at weekends. There are also cafes five minutes away on the road towards the botanical garden.

Planted in 1808 to acclimatise spice plants brought from the East, and still a working research institution. The avenue of royal palms is the photograph; the orchid houses, the Amazon section and the resident marmosets are why it takes two hours.

A Calatrava building like a fish skeleton reaching out over the water, holding a science museum about what the next fifty years do to the planet. Short, well made, and unusually direct about Brazil's own part in it.

Found under a car park during the port works in 2011: the stone quay where slave ships unloaded in the early nineteenth century, close to a million people through this one wharf. A small excavated pit with very little to look at, and the most affecting thing in Rio.

The lanes around Travessa do Comercio are lined with old bars serving a set lunch to office workers: cheap, fast and good. Anything advertising comida a quilo is the safe bet.

A concrete cone 75 metres high, built through the 1960s and 1970s and modelled on a Mayan pyramid, which sounds terrible and is not. Four stained glass strips run floor to ceiling on each face over a vast, coloured, almost empty interior.

A staircase of 215 steps that the Chilean artist Jorge Selaron tiled with pieces sent from all over the world, and kept changing until he died on them in 2013. Busy from mid morning, so earlier is better.

A yellow open-sided tram that has been climbing this hill since the nineteenth century, running from the centre over the arches of the old aqueduct into Santa Teresa. It costs almost nothing and the ride is the attraction.

The two small squares on the ridge hold most of the neighbourhood's restaurants. Several do a proper Bahian moqueca, which is worth ordering if the rest of your trip is not going north.

An old grocery shop turned into a bar, still with its high ceiling and its wooden shelves to the roof, pouring beer properly cold to a room of regulars. Everyone knows it as Bar do Gomes, after the family who kept the shop, rather than by the name over the door.

396 metres of bare granite in the mouth of the bay, climbed by two cable cars running since 1912. The middle station has a terrace and a bar and half the view; the summit has the rest, beaches on one side and the bay and mountains on the other. Stay for the lights.

Two and a half kilometres of waterfalls in a great curve of forest, and the Brazilian side is the one that shows you all of it at once. A single walkway follows the gorge to a catwalk under the main drop. Late afternoon light is the best of the day and the coaches have gone.

A private bird park opposite the entrance to the national park, with walk-in aviaries you share with toucans, macaws and harpy eagles, most of them rescued. An hour, and better than it sounds even if birds are not your thing.

The town has an outsized number of large steakhouses, a legacy of coach tourism, and several are genuinely good value. Order the rodizio and let them keep bringing it.

The head of the gorge, where about half the river goes over an eighty metre drop in a single horseshoe. Reached by a small park train and then a kilometre of catwalk across the flat water above it. Go first thing: the platform is small and the queue for it is not.

A walkway running over the crest of several falls, with the river dropping away under the grating and the spray coming back up through it. Flat, easy and about an hour and a half.

There are cafes and a buffet at the main station and snack bars along the circuits. None of it is memorable and all of it saves an hour, which on this day is the right trade.

The lower circuit, which winds down through the forest to the base of the falls and puts you close enough to be soaked by several of them. Steps and slopes, about two hours, and the boat that runs into the spray leaves from here.

Lina Bo Bardi raised the entire gallery off the ground on four red columns so the view down the avenue was not blocked, and hung the paintings on freestanding glass easels so you walk between them and can see the back of every canvas. Raphael and Bosch through to Portinari.

A block of original Atlantic forest left standing across the road from the museum since 1892, with huge trees, cool air and marmosets in them. Twenty minutes here is the best possible recovery from an airport.

Jardins starts one block southwest of the avenue and is where the restaurants are, at every price from a counter selling coxinha to somewhere that needed booking a month ago. This is the best eating city in South America, so start now.

Two Jesuit priests said the founding mass here on 25 January 1554, in a hut on a ridge between two rivers, and all twelve million people out there are downstream of that. The reconstructed church and small museum take half an hour, and the courtyard cafe is a good place to start.

A 1940s bank headquarters built in open imitation of the Empire State Building, with a public observation deck at the top. The view is the reason: towers running out past the horizon in every direction, which is the only way to grasp the size of this place.

The lanes off Rua Direita and the arcades around Praca do Patriarca are full of counters feeding office workers fast and cheap. Ask for the sanduiche de mortadela if you want the thing the centre is famous for.

The state art collection, in a heavy brick building from 1900 that was stripped back to its shell and roofed in glass in a famous restoration. Brazilian painting and sculpture from the colonial period to now, and the best place anywhere to see it.

A square and a half kilometre of lawns, lakes and paths in the middle of the city, with Niemeyer's white pavilions and their linking canopy at the northern end. Free, open early, and at its best on a Sunday morning.

Three floors inside one of the Niemeyer pavilions, tracing five centuries of African presence in Brazil through slavery, religion, work, music and art. The most important museum in the city and it needs two hours.

The streets around Rua Aspicuelta have bakeries, botecos and small restaurants at every corner. A pastel and a sugarcane juice from a corner bar costs almost nothing and holds until dinner.

A dead-end lane where every wall, gate and shutter is painted and repainted by whoever turns up with the aerosol, so it is never the same twice. Ten minutes to walk, longer if the light is good, and the bars at either end are why you stay.

Niemeyer designed it in the 1950s and it took until 1966 to finish: the largest residential building in Latin America, a curved slab with its own postcode, laundries, shops and a residents' association that behaves like a small town council. Walk the arcade underneath and look up.