On Avenue Paulista you can take one of the public buses (next to the tourist office), and visit Ibirapuera Park, one of the biggest city parks in the world. You can also get to Ibirapuera Park by taxi.
Ibirapuera Park is a very good place to spend half a day away from the traffic of São Paulo. In order to visit the park, it is advisable to rent a bike, the park is huge.