What's a good 3-day itinerary for Rio de Janeiro?

Day 1 stays in Centro and Santa Teresa, about 7 km of walking on flat ground plus one steep hill. Start at Confeitaria Colombo on Rua Gonçalves Dias by 9am. The stained-glass ceiling dates to 1894 and the café com leite costs R$14, about $2.70. From there it's a 10-minute walk to the Museu Nacional de Belas Artes on Avenida Rio Branco, free on Sundays. Head south to the Catedral Metropolitana by 11:30. The 1979 concrete cone seats 20,000 and the interior is dark and cool, a relief from Rio de Janeiro's midday warmth. Take the bonde streetcar from Largo da Carioca uphill to Largo do Guimarães for lunch at Bar do Mineiro. Mind you, the feijoada runs R$65 for a portion big enough for two. Walk the cobblestones down to the Escadaria Selarón, 215 tile-covered steps, by 3pm. End in Lapa for a cold chopp at Bar Belmonte around 5pm, R$12 for a tall glass.

Day 2 runs along the Zona Sul coast, about 8 km plus the Sugarloaf cable car. Walk Copacabana's 4.5-km promenade early, before 8am, when the mosaic sidewalk is still damp and the kiosks are putting out fresh água de coco for R$8. Breakfast at Café 18 do Forte inside the Forte de Copacabana, where the view of the beach curve costs nothing beyond a R$22 coffee and pão de queijo. Cross the Arpoador rocks to Ipanema by 10:30. The surf break at Arpoador is loud. Posto 9 tends to fill up fast, but before noon you'll still find space. Lunch at Zaza Bistrô Tropical on Rua Joana Angélica around 1pm, where the moqueca runs about R$95. Take a taxi from Ipanema to Praia Vermelha in Urca, 15 minutes, R$20-25. Board the Sugarloaf cable car by 4pm. The last light hits the granite face around 5:30pm in June, and you can see the full bay from 396 metres. Dinner at Garota de Ipanema on Rua Vinícius de Moraes, the bar where Tom Jobim wrote the bossa nova in 1962.

Day 3 climbs to Cristo Redentor and comes back down through green Rio de Janeiro. Book the 8am Corcovado train from Cosme Velho station. The 38-metre statue, completed in 1931, stands at 710 metres on Corcovado. At 8am you'll share the platform with maybe 40 people instead of the 400 who arrive by 10. The air is cooler up there, often 5-6°C below the coast, and the smell of wet forest canopy hangs heavy after overnight rain. Come back down by 10:30 and stop at Parque Lage at the foot of Corcovado. The 1920s mansion has a courtyard café, and the Cristo statue is visible above the treeline. Lunch at Braseiro da Gávea on Praça Santos Dumont around noon. The picanha for two costs R$140 and arrives sizzling on a hot plate. Spend the afternoon at the Jardim Botânico, founded in 1808 by Dom João VI. The imperial palm avenue runs 750 metres and the R$15 entry is one of Rio de Janeiro's best values. End at Lagoa Rodrigo de Freitas by 5pm with a bike rental, R$10 per hour, on the 7.5-km lagoon path.

Travel between clusters costs R$15-30 by taxi or Uber per hop. The Metrô runs from Copacabana through Centro on Line 1 for R$6.90 per ride. June is Rio de Janeiro's dry winter season, with highs around 25°C and cool mornings near 17°C. You won't need sunscreen before 10am but you will need it by noon. Carry a light jacket for Corcovado and for air-conditioned restaurants. That said, Portuguese goes far here. Por favor and obrigado open most doors, and Google Translate handles menus at sit-down places. Total across three days is about 28 km on foot, with 3-4 short taxi rides between clusters.