Rio de Janeiro on $25, $80 or $300 a day

Cristo Redentor (Christ the Redeemer, R$92 by van from Cosme Velho station, R$82 by cog railway - book online; the 38m statue on the 710m peak, the view over Guanabara Bay and the city below. Arrive early - clouds roll in by 10am). Allow 2 hours.

Sugarloaf Mountain (Pao de Acucar, R$130 return cable car - two stages: Morro da Urca then the summit at 396m; the view at sunset is arguably better than the Christ). Or visit the Urca neighborhood below the cable car (quiet, local, excellent seafood restaurants).

Arpoador sunset (free) between Copacabana and Ipanema - the ritual of clapping as the sun disappears below the mountain. Beachside caipirinha (R$15-20). Dinner at a Ipanema botequim: a prato feito (the standard Brazilian plate: rice, beans, farofa, a meat, R$25-35).

Bonde tram to Santa Teresa (R$25). The Escadaria Selaron (free). The Museu Chacara do Ceu (R$10 Tue-Sun, free Thu). The hillside streets and the views over the city from the Santa Teresa miradouros (viewpoints). Breakfast at a Santa Teresa cafe (acai bowl R$20, fresh coconut water R$8).

Walk down to Lapa (15 min downhill through the arches). The Real Gabinete Portugues de Leitura (free - the most ornate library in Brazil, neo-Manueline interior). Lunch at a Centro botequim (feijoada on Saturday - the Brazilian black bean and pork stew, R$30).

Lapa on a Friday or Saturday night: the street samba is free. Pick a bar, order R$8 caipirinhas, and join the dancing. The Circo Voador live music venue (R$30-60) has the best samba shows. Walk back to Copacabana or Uber (R$20).

Pedra da Gavea or Trilha do Corcovado hike (free trails through the Tijuca National Forest - the world's largest urban forest. The Corcovado trail takes 2-3 hours each way; start before 7am). Or: the Dois Irmaos trail above Vidigal favela (the best view in Rio, 1.5h each way, free but go with a guide organized through the favela community for safety).

Ipanema beach afternoon (free - bring cash for the beach vendors: mate tea R$5, coconut water R$10, queijo coalho cheese grilled on a skewer R$8). Posto 9 for the atmosphere.

Ipanema bar crawl: Baretto-Londra, Garota de Ipanema (the bar where the song was written), and a botequim on Farme de Amoedo. Dinner: a kilo restaurant (pay by weight, R$50-70 for a full plate).

Christ the Redeemer (R$92, early booking) then Sugarloaf Mountain (R$130). The two iconic viewpoints in one day - do Christ in the morning (clearer before the clouds), Sugarloaf at sunset (the city lights below as darkness falls).

Lunch at a Botafogo restaurant (the neighborhood between Sugarloaf and Ipanema: excellent restaurant-to-price ratio, R$50-80 for a full meal). Afternoon at the Museu do Amanha (R$30) on the renovated Porto Maravilha waterfront.

Dinner at Zaza Bistro Tropical in Ipanema (R$100-140pp, Brazilian-international, the neighborhood's most atmospheric restaurant). Caipirinha at Devassa or Bar Astor (classic carioca bars) after.

Community tour of Rocinha or Vidigal favela (R$80-120 with a resident guide from an established community organization - organized through the hotel concierge). The largest favelas in Brazil: extraordinary street art, the organic architecture climbing the hillside, and a genuinely different perspective on Rio. The guides are residents and the income goes directly to the community.

Jardim Botanico (R$20) in the afternoon heat - the shaded paths and the imperial palms. The lagoon jogging path walk (free). Lunch at a Jardim Botanico restaurant (R$60-80).

Rio's live music: a samba show at Rio Scenarium in Lapa (R$45 cover + drinks - three floors of antiques and live samba, one of the great music venues in Brazil; reserve ahead on weekends) or jazz at Jazzmania.

Bus or organized trip to Buzios (3h, R$60 each way or R$200pp organized tour): the peninsula resort town 190km east of Rio. 23 beaches, clear water, good snorkeling, and the most glamorous beach scene in Brazil outside Florianopolis. Brigitte Bardot put it on the map in 1964.

Beach afternoon at Praia do Ferradura or Praia da Tartaruga. Lunch at a Buzios seafood restaurant (R$80-120 for fresh fish and lobster - genuinely cheaper than Rio).

Return to Rio or stay overnight. Farewell dinner at Marius Degustare (R$150-200pp - the finest rodizio (unlimited service) restaurant in Rio; the seafood version is the highlight: unlimited shrimp, oysters, crab, fish, arriving continuously at the table).

Private helicopter tour (R$800-1,200pp for 30 min: Christ the Redeemer, Sugarloaf, the beaches of the South Zone, and Guanabara Bay from the air - the most spectacular urban panorama in the world seen from the best angle). Breakfast at the Copacabana Palace (the grand hotel of Rio since 1923) or the Fasano Rio.

Lunch at Roberta Sudbrack (the most refined contemporary Brazilian cuisine in Rio, R$300-400pp for the full tasting menu). Private afternoon: a capoeira lesson with a Mestre on Ipanema beach, or a private samba lesson with a Mangueira school dancer.

Dinner at Fasano Al Mare (the Fasano Hotel terrace restaurant, Ipanema beachside, R$350-500pp for fish and wine with the sound of the Atlantic below). Cocktails at the Fasano rooftop bar.

Private speedboat to Ilha Grande (2h south - the island nature reserve with no cars, pristine Atlantic Forest, and the clearest water in Rio state). A private naturalist guide for hiking to the Lagoa Azul (Blue Lagoon) or Lopes Mendes (the most beautiful beach in Brazil).

Snorkeling lunch on the boat: fresh fish grilled on deck, cold beer and coconut water, anchored above a coral reef. Afternoon swim at Praia do Aventureiro (accessible only by boat, no roads).

Return to Rio at sunset. Dinner at Olympe (Chef Claude Troisgros's Rio flagship, R$400-600pp - the finest French-Brazilian cuisine in the country; reserve 2 weeks ahead). A final caipirinha at the Copacabana Palace bar.

Chauffeured trip to Petropolis (1h30 north into the mountains): the former imperial capital, the Museu Imperial (the last emperor's summer palace, R$30 - the Brazilian crown jewels, the imperial crown with 639 diamonds), and the Palácio de Cristal. The mountain air (18 degrees C) is a relief from Rio's heat.

Lunch at a Petropolis restaurant (the mountain region cuisine: fondue, trout, cold cuts). Return to Rio. Final shopping: Ipanema boutiques for the best Brazilian swimwear (the bikini was invented here), Havaianas flagship store.

Farewell dinner at Oro (1 Michelin star in Leblon, Felipe Bronze's contemporary Brazilian, R$400-500pp for the tasting menu - one of the finest expressions of modern Brazilian cuisine). Sunset cocktail first at the Arpoador with the cariocas.