A bit further away from the center, but reachable by metro, too, is the Avenida Paulista. It is one of the most important avenues in São Paulo, with many headquarters of the financial and cultural sector. Also there are many possibilities for shopping or dining. The Avenida Paulista is mainly flanked by skyscrapers, but still a few mansions of coffee barons exist (as in the Avenida Brasil, too). Only worth visiting today is Casa das Rosas. This mansion is located at the beginning of the Avenida Paulista and has turned into a cultural center. A big highlight on the Avenida is the MASP (Museum of Art in São Paulo), with a a small native forest park on the other side of the avenue. A link to the program of the MASP in portuguese | more about MASP in wikipedia).
The São Paulo Gay Pride Parade in May/June, considered the largest in the world, and the São Silvestre Marathon on New Year’s Eve take place on this avenue yearly. Celebrations of local soccer teams and world cup championships as well as political demonstrations also have the Paulista as a stage. (from wikipedia, more about the Avenida Paulista in wikipedia).
Another Avenue is the Avenida Brigadeiro Faria Lima, these days planned to be reachable by metro (yellow line). It is in direct competition with the Avenida Paulista, as here too is a big financial and commercial area. The Shopping Iguatemi is one of the best shopping centers of the city, with some restaurants and especially exclusive shops with french or italian fashion as Louis Vuitton, Chanel, Gucci and others, also Tiffany is here (site of Shopping Iguatemi). The Museum Casa Brasileira in the avenue is showing decorative and historic art.
A street for shopping is the Rua Oscar Freire. It is listed as the 8th luxurious street in the world, and after 5th Avenue in New York the second luxuriuos in the Americas (more in wikipedia).
If you like football/soccer, a visit of the museu do futebol is a must. It is located in the Estádio Municipal Paulo Machado de Carvalho, also known as Estádio do Pacaembu (wikipedia). Opened in 2008, it offers many interactivity. Have an impression watching the youtube video.