Yes, there are serious outdoors in Mexico City. In fact, national parks surround almost the entire city. There are also protected areas and parks nearby in the State of Mexico, and to the south, the wilds of Milpa Alta and Tlalpan.
The topography of mountains and volcanos makes it a natural marvel, if not necessarily, a nature destination. This may be changing.
The Mexican Federal Government has designated ten natural protected areas in, and immediately surrounding the City. A few are smaller natural areas that need restrictions to prevent their being overrun. Still more are full-blown national parks.
As more and more international visitors discover what Mexico City has to offer, the City is coming into its own as an outdoor and adventure destination. Where else can you get this much nature this close to a massive city?
For serious outdoors in Mexico City, very little public transportation infrastructure will get you truly close. With a little ingenuity, they're all within reach, though. Some parks have ancient archaeological digs or colonial period ruins. Some of the same have astounding mountain ranges, cliffside views, and places for all levels of exploring.