There used to be ping pong tables in the billiards, but most of them have closed down. I don't know if there's one still open near Cuatro Caminos or Alvarado in Bravo Murillo. It looked like a bussiness in decadence 2 years ago.
I played in Universidad Autónoma de Madrid, in the polideportivo, but it's 8 years since I finished studying. Maybe Universidad Complutense also have, and it's closer to the town. You can ask also in some Polideportivos municipales.