As will be the case anywhere in Brazil, one of your best bets for a true cultural experience will be to attend one of their football matches. Depending on the time of the year, you'll be able to catch any of the major teams from Sao Paulo (Santos, Sao Paulo, Palmeiras, and Corinthians)in the Campeonato Paulisto state league or the national Campeonato Brasileiro.
Often the best Brazilian teams come from Sao Paulo, with both Santos and Palmeiras holding the Brazil A-league title 8 times, while Corinthians are Brazil's richest club and current champion. If you want to catch a match, Sao Paulo play at Morumbi stadium, Corinthians play at New Corinthians Stadium, Palmeiras play at Arena Palestra Italia (although it is under construction until the summer of 2013), and Santos play at the smaller Estadio Urbano Caldeira.
For the locations of these sites, when matches will be held, and the cost of tickets, consult each team's website!