Parque Estadual da Cantareira protects a huge swath of Atlantic rainforest on the northern edge of São Paulo. It feels far removed from the city, with shaded trails, dense vegetation, birds, and occasional views back toward the urban sprawl.
This is a place for walking rather than picnicking. Take water, check which park nucleus is open before you go, and give yourself time for the transport: the forest is part of São Paulo, but it sits well beyond the usual museum-and-restaurant circuit.