São Paulo Museum of Modern Art
at Ibirapuera Park, Pedro Alvares Cabral Av s/n it's a good program. always show interesting exhibitions, and is situated inside Ibirapuera Park (where you can walk and enjoy nature (and movement also, at the weekends)), also has a nice (and not so expensive) restaurant.
Museum of Modern Arts of São Paulo, featuring a lot of temporary art shows. Check the program beforehand or dive randomly in an artist's collection ;) Ideally located in Ibirapuera, ideal on a nice day, to mix culture and nature.