Rio de Janeiro

Two cable car stages reach the 396m granite dome. From the first station a short rock path lets you climb the rest on foot.

A statue 38m tall stands on a peak of 710m, reached by rack railway. Cloud settles often enough that some days the summit shows nothing at all.

Four kilometres of sand run beside a pavement laid in black wave patterns. Numbered lifeguard posts divide it, and people arrange to meet by those numbers.

The sun goes down behind the rocks at the western end, and the beach applauds when it does. The surf runs harder than at Copacabana, which draws the boards.

A Chilean artist covered 215 steps in tiles sent from around the world. People still post tiles in, so the surface keeps changing.

A yellow tram climbs the narrow hill roads past old mansions on the lanes. Walking it in daylight, when fewer people are about, is the advice given.

Laid out in 1808, with an avenue of royal palms running 750m. Monkeys and toucans are in the trees, so bags are kept closed.

An eighteenth century aqueduct now carries the tram across its top. The square beneath fills with music and people on weekend evenings.

A forest inside the city, replanted in the nineteenth century after the coffee was cleared. Waterfalls and lookout rocks sit along the trails, and monkeys come to the path.

Built for the 1950 world cup and still hosting the big matches. On days without a game a guided round takes you into the dressing rooms and onto the turf.

Calatrava's design, which since 2015 has stood on the pier past Praca Maua. Roof solar fins follow the sun; exhibits explore climate and humanity's future. The waterside walk behind it looks across the bay to Niteroi.

Brazilian artist Eduardo Kobra painted these five giant faces on old warehouse walls for the 2016 Olympics. They depict indigenous peoples of five continents on the Olympic Boulevard, the redeveloped port walk. Step back to the water to fit the wall in.

Opened in 1909 and modelled on the Paris Opera. It faces Cinelandia square, and on non-performance days, daytime guided tours take in the gilded foyer and the auditorium. The basement keeps an old restaurant dressed in Assyrian-style tiles.

Portuguese immigrants built this library in 1887; behind its Manueline stone front, 3 tiers of shelves reach the ceiling. It holds the largest Portuguese-language collection outside Portugal. Its sign on a downtown side street is tiny, so people walk past.

You run off a ramp high in the Tijuca forest on a tandem hang glider with an instructor and land on Sao Conrado beach. Flights last around 10 minutes and wait for the right wind. Non-flyers can drive up to the ramp for the view of Pedra da Gavea and the sea.

The twin peaks rising at the end of Leblon beach, reached by a trail that starts above the Vidigal community. About 1 hour up, Ipanema, the lagoon and Corcovado all come into one view. Most hikers take a moto-taxi from the bottom of Vidigal to the trailhead.

A saltwater lagoon behind Ipanema, linked to the sea, ringed by about 7km of cycle lane and footpath. Lakeside kiosks serve dinner while the Christ statue on Corcovado lights up. Rental stands on the shore hire out swan pedal boats and kayaks.

A 1920s mansion in the forest below Corcovado, famous for its arcaded courtyard around a pool. The house today holds a school of visual arts. A trail up to the Christ statue begins deep inside the park, with chains on the steep parts.

A cone of concrete completed in 1979. Four bands of stained glass climb the walls and join overhead in a cross. It is 5 minutes' walk from the Lapa Arches, and inside it stays cool despite how it looks from the street.

Rock-cut steps in the old port district, named for the salt unloaded here by enslaved workers. Samba, the story goes, took shape in the gatherings here, and evening sessions still play under the rock. On busy nights carry your bag in front.

The stone wharf where enslaved Africans were landed, inscribed on UNESCO's heritage list in 2017. Port works uncovered it in 2011, and visitors peer at the stones over a low fence. With nearby Pedra do Sal it makes one walk through "Little Africa".

On Praca Maua, the museum joins two buildings, an old palace and a former bus terminal, under a wave-shaped roof. Shows cover Rio's past and its street art. Up top, a terrace faces the harbour and the Museum of Tomorrow.

An island deep in the bay, about 1 hour by ferry from Praca XV, with no cars. You loop it by bicycle or on foot past small beaches and old houses. Weekend ferries fill with locals, so weekdays are quieter.

Niemeyer's saucer-shaped museum, opened in 1996 on a cliff across the bay. The round gallery windows frame Sugarloaf and the city over the water. Take the ferry from Praca XV, then a bus or taxi.

A fort finished in 1914 on the headland closing off Copacabana to the south, now an army history museum. From the ramparts the whole beach curves like a bow. A café inside makes it a good spot for early morning coffee over the sea.

A mountain town some ninety minutes' drive up from Rio where Brazil's last emperor kept his summer palace. The palace is now the Imperial Museum, displaying his crown and carriages. It sits much higher than Rio and runs cool, so bring a layer.