There are several places not far from Madrid where it should be not very difficult to find it: just to say a few the Dehesa Boyal near San Sebastián de los Reyes, the Dehesa de Sacedón and Camino de la Zarzuela (both between Sevilla la Nueva and Villaviciosa de Odón, along Guadarrama river). Farther away you have the path climbing to Navahonda Hermitage near Colmenar del Arroyo, the dirt track for cars along the east side of San Juan reservoir, or along the road and tracks going from Fresno de Torote to Ribatejada, as well Puente Mocha at Valdemaqueda (by river Cofio) and around Chapinería (for instance, the dirt track starting between Chapinería and Navas del Rey along a small creek), both already mentioned.
Explore for example eBird for the species, using the "Large" map and ticking the "Show points sooner" box
I have not suggested going to El Pardo as a first option because, although being the stronghold for the species at Madrid, you cannot enter inside it, so you can just go to outside the perimeter and look from some vantage point. The only one that you can find easily -Mingorrubio, at the southern end- uses to be a little crowded. But if you don't have enough time or a car, it is still a very good choice going straight to Mingorrubio or perhaps walking along the "Corredor de Somontes" from Somontes to Mingorrubio and the dam of El Pardo reservoir.