Cantareira State Park (Parque Estadual da Cantareira)

Covering nearly 20,000 acres and rising out of northern São Paulo, Cantareira State Park (Parque Estadual da Cantareira) is one of the world’s largest patches of tropical rainforest that's within a city. A popular spot for escaping the hustle and bustle of the city on the weekend, visit Cantareira early on a Saturday morning to leave the crowds behind, then take your pick between the park trails which vary in length from 300 meters to 10 kilometers. 
Split into four quarters — Pedra Grande, Águas Claras, Engordador, and Cabuçu — the Engordador section is best known for its waterfalls where you can go swimming. As you wind through the forest trails, look out for howler monkeys, Brazilian hawks, and endangered tropical plants like imbuya phoebe, black cinnamon, and canela-sassafrás. 
A UNESCO bio reserve that's home to the only species of pine native to Brazil, one of the most popular trails through Cantareira is to Pedra Grande (Big Rock) — a fairly steep 1-2 hour hike, and from the top you can see the whole of São Paulo spread out before you. Rest at the nearby picnic tables, and bring some snacks. A further 1.5 km along is a nice lake. And on the Nucleus Engordador trail you can ride your mountain bike along the trails. Just remember to bring your helmet! 

Practical Info

Cantareira State Park is in the north end of São Paulo, about 45 minutes' drive from downtown when there's no traffic. The closest metro station is Tucuruvi. Entrance to the park is from Tuesday to Sunday, 8am-5pm (last admission at 4pm), and entry costs R$9. To decide where you want to go, check out the map showing the different trails at the park's entrances.