There are paths to wander on, although some sections were closed the day we went there. The rose garden was beautiful but not all that fragrant. The park's main drawback is that there is only one entrance to the park on the road across from Rio Manzanares (Paseo de la Virgen del Puerto), so it's important to keep that in mind as you wander through the park. You either need to retrace your steps or walk on one of the paths that more or less circle through the park. There is a convenient restroom right next to the entrance. You need to walk down steps in order to access the park. It is a quiet, relaxing place to visit and a lot less crowded than El Retiro.
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