When I was looking for a place to live in Madrid nearly two years ago, I based it largely on living near a park where I could go running. I ended up near the Parque del Oeste (map), which I have completely fallen in love with. I call it mi parque and I really do feel a sense of propriety about it. I know the early morning dog walkers, the older couple who hit a tennis ball back and forth on one of the trails, the parks maintenance workers in their fluorescent yellow and blue outfits.
Parque del Oeste slopes downhill from Moncloa and runs along the western edge of the city. It's great for running because of the dirt paths, the hills, and the lack of cars. It's also a perfect place to go for a stroll, lie in the grass, read on a bench, have a picnic, or box (?! left).
Parque del Oeste is quite different from the famed and (also) beautiful Parque del Buen Retiro. To begin with, it's not in the center of the city and therefore attracts much less traffic. I like to think of it as a little "wilder" than Retiro, in part because it's a little more off the beaten path. Though it's still quite a civilized place; so civilized, in fact, that it is home to a rosaleda (rose garden), which this year was absolutely fantastic. Seems that the cool, rainy spring we've had here has done wonders for the roses, which (when I went to see them two weeks ago) were in full bloom and stunning.To check out the Parque del Oeste, I recommend starting at one of its ends: (the Moncloa metro/bus station or the Templo de Debod) and wandering.