South West. Metro Chapultepec
The main reason to head over here is the city's Museum of Anthropology, but if you wanted to avoid the crowds, or just weren't in the mood for yet more pottery, cross the Paseo de la Reforma and get lost in the park. It's apparently the largest urban green space in the whole of Latin America. It's defintely the place to come if you're running low on cheap Mexican wrestling masks or pork scratchings, as they're on sale about every four yards.
Anyway, one way to escape the visitors, and vendors of pig-based snacks, is to delve deeper into the wood and go rambling there. But a more rewarding alternative is to hike up the hill to the castle, which was once the summer house of Porfirio Diaz (http://en.wikipedia.org/wiki/Porfirio_Diaz), then later a military training academy and now a marvellous history museum. It also has a superb mural by David Siquieros, one of Diego Rivera's contemporaries, who also became famous for his involvement in the failed assassination attempt on Leon Trotsky, in the south of the city, for (I believe) not being communist enough.
On the top floor of the building you come out onto a superbly maintained roof garden, with great views of the city. Here, especially mid-week, is where you will get your fix of calm.
In the park, but nearer to the Anthropology Museum, is where you'll catch the 'flyers' who practice every day.