El Retiro Park
There are two places I found to run while in Madrid, both slightly outside El Centro (we stayed in Salamanca). The first was the best – El Retiro Park.
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El Retiro Park is about a 1 km by 1 km park filled with dirt and paved paths criss-crossing throughout. It’s easy to get in a 6-8 km run without seeing the same thing twice. There is a small lake (really more of a pond) and a glass palace, as well as various fountains and sculptures scattered throughout the park.
Paseo de la Castellana
The second location is the Paseo de la Castellana. It starts in the south as Paseo del Prado, as you go north it becomes Paseo de Recoletos, and finally is called Paseo de la Castellana. This road is a major artery that runs north-south through the city. in the middle of the road is a wide green and walking space. It’s all paved, though you can run on the grass, and pedestrians have right of way on the few small roads that cross the median (no lights; cars just stop and look for pedestrians).
A third possibility, which I did not try because it’s a little ways outside the center of the city, is Casa de Campo. It’s a massive park (maybe 5-6 kilometers per side) and west of the Palacio Real de Madrid.