Circle the lagoa at dusk

Run, walk, hire a tandem or pedal a swan boat around Rodrigo de Freitas Lagoon, known to everyone as simply the lagoa, for one of the simplest but most pleasant evenings you can spend in Rio. Stop along the 7.4km course way for fresh coconut juice, a cold chope (draught beer) or an evening meal at one of the lakeside restaurants (my favourite is Arab da Lagoa, which serves hummus and pitta). While taking in the famous landmarks (Christ the Redeemer, the Dois Irmãos and Pedra da Gávea mountains) and the Rio cliches of footballers, skateboarders and keep-fit fanatics, keep your eye out for wildlife, especially herons and capybara - the world’s biggest rodent. The water’s notoriety for stinking pollution and dead fish is not undeserved, but is usually only noticeable one month a year. As far as possible, however, avoid driving anywhere near the Lagoa. The traffic is a nightmare.

Picnic on the Dois Irmãos

Rio is a city of spectacular views, but few can match the vista from the Dois Irmãos (Two Brothers) mountain, which looks down over Ipanema and Leblon and out to the Atlantic horizon. Start early to miss the crowds, pack a simple lunch, take a combi (minibus) up through Vidigal favela, then hike through the forest for 40 minutes to the peak, where you can feast your eyes while filling your stomach. Once you are back down at sea level, cool off by jumping in the sea. Just be aware that the security situation in Rio is in flux so even though Vidigal has long been one of the safest favela communities, it is worth asking around whether this is still the case before setting out.

If this gives you a taste for more adventurous hikes and still more incredible panoramas, try climbing the Pedra da Gávea, strolling up the Bico do Papagaio (Parrot’s Beak) or – further afield in Rio state – visiting Paraty’s Ponta Negra or hiring a guide for the stunning two-day mountain trail from Teresopolis to Petropolis.

Have a sundowner on the Urca seawall

It has been called Rio’s Malecón, but that does not do justice to the sea wall on the Urca peninsula, where crowds gather outside Bar Urca (which does great salgadinhos, or snacks) every Friday night to watch the sun go down behind Christ the Redeemer on the Corcovado, then drink and talk into the early hours. The vibe here is extremely relaxed. This is partly thanks to Urca, which feels more a 19th-century fishing village than a district in one of the world’s biggest cities. There is also an unusually low threat of crime because the peninsula is controlled by a military base. For a variation on the same theme, hike 15 minutes up the Morro do Urca to one of the bars serving caipirinhas on the ropeway route up to the Sugarloaf. Other decent drinking holes in Rio include Bar do Gomez in Santa Teresa, Adega Perola in Copacabana and Bar do Zé in Catete.

Samba at Pedra do Sal

Outside of carnival, samba does not get much better than the weekly free performances at the Pedra do Sal (Salt Rock) in the neighbourhood of Saúde. This is hallowed ground – a former centre of the slave trade that later became home to a liberated “Little Africa”, a quilombola community and many of Brazil’s finest musicians. Each Monday – and sometimes on Fridays – these streets fill with rhythm, revellers and hawkers of food and beer. To make a full day of it, go early and check out the Museum of Tomorrow and the impressive Olympic redevelopment of the port district, and then stay late for more drinks, sounds and dancing at the nearby Trapiche Gamboa samba nightclub.

Wander up Selarón’s mosaic stairway in Lapa

One of Rio’s most beautiful, sad and mysterious stories of recent times was the death of Chilean artist Jorge Selarón, who decorated a stairway in Lapa with mirrors, mosaics and ceramic tiles. This labour of love was created over two decades, largely without official recognition. But once fame struck so did tragedy. Selarón, who previously used to drink in the street bars nearby, was found dead on his steps in 2013. Whether it was murder or suicide is still debated. But visitors can still admire his work on the way up from the live forro and chorinho music echoing through the arches of Lapa up to the bohemian bars and restaurants of Santa Teresa. NB: don’t walk about at the top of the staircase at night.

Christ on a bike

There are numerous ways of reaching the Christ the Redeemer statue. You can go by minibus or train from Cosme Velho, or hike up from Parque Lage. But, for me, nothing is as satisfying as a cycle up to the iconic peak through Tijuca forest. It is a tough climb, but the reward is glorious scenery, occasional wildlife (capuchins, toucans and snakes), mountain showers and then an exhilarating ride down some very steep slopes. More ambitious riders can make a morning of it and do the three-hour circuit from Santa Teresa, up to Corcovado, along the Paineiras ridge, down to Alto da Boa Vista, then up and down part of the brutal Olympic cycling course past the Mesa do Imperador and Vista Chinesa. Bikes can be rented at Fiets Rio in Ipanema or Laranjeiras.

Fish lunch at Niteroi market

Unless you are crazy about barbecued beef, Rio’s restaurants can be a disappointment, but head a little out of the city and there are some excellent dining options. One of the liveliest is in the market at Niteroi (a short ferry ride across Guanabara Bay from central Rio), where fishmongers on the ground floor sell a wide range of fresh seafood that you can then have cooked in the style of your choice at the restaurants upstairs. Other good eateries include Os Esquilos, deep inside Tijuca forest, and Arataca in Copacabana, which looks small and unremarkable but does an excellent moqueca (seafood stew from Bahia) and one of the best tambaqui (a freshwater fish) meals you will find outside the Amazon. Oh, and while we are on the subject of food, try a breakfast of açai fruit mixed with banana and granola at one of the many juice bars in the city.

Stroll among the bromeliads at Jardim Botânico

For full immersion in the lush green of this tropical city, it is hard to beat the 200-year-old botanical garden. I am no expert, but have returned several times to wander the extensive grounds and wonder at the extraordinary diversity of the 6,500 species that grow here, including carnivorous plants, orchids, cacti and bromeliads. After a tough afternoon of selfie-taking on the Avenue of Royal Palms, relax at one of the coffee shops or escape the heat in the forest shade. If that whets your appetite for an even deeper green experience, make a day trip to the home and gardens of Burle Max at Barra de Guaratiba (see below), an ecologist, artist and landscape designer who – for me – should be Brazil’s most celebrated son. Shunning the once prevailing trend to import European flora and designs, he mixed folk art, cubism and abstractionism to create a distinct tropical garden style that celebrated the beauty of indigenous plants, such as philodendrons and bromeliads. If that was not enough, he was also among the first to call for conservation of the Amazon.

Tapioca pancakes at Gloria market

With its transgender sex workers, sex hotels and shoddy bars, Gloria is among the more colourful of Rio’s neighbourhoods, but it truly comes into its own each Sunday morning with the best food market in the city. From the self proclaimed “Rei da Merda” (King of Shit) manure seller to the spice traders offering dozens of different types of chilli, the stalls are a riot of colour, sound and smells. For a classic snack, sit at a plastic chair and chow down on a tapioca pancake. My current favourite is the savoury tomato, cheese, onion oregano, but sweeter tooths may prefer the Nutella and banana. It is good, filling food, especially when washed down with a fresh orange juice. If it is souvenirs and gifts you are after, however, you might be better off at Ipanema’s Sunday hippy market near General Osorio station which is something of a craft fair.

Stand-up paddleboarding at Barra de Guaratiba

I cannot pretend to be any good at this sport, but if the conditions are right, it is one of the few beach activities I enjoy. At Copacabana and Arpoador, the waves are usually too big for beginners like me and frankly the water quality is sometimes so filthy I would not recommend anyone risk falling in on a murky day. But drive an hour or more away from the city’s tourist districts and it is possible to find calm, clean seas. My favourite is the mangrove swamps at Barra de Guaratiba (not on map), which is perfect for first timers. With a little luck, you might even see an alligator – though thankfully they usually do not grow big enough here to be worthy of a wobble. On the way home, stop for with a meal at the nearby Point de Grumari restaurant, which has a superb seafood platter and – because it is on a hill by the coast – one of the best views of mangrove swamps you will get anywhere in the world.

• This article was corrected on 27 April 2017 to comply with Guardian style guidance on transgender people and sex work.