The Alduccio's that I knew years ago started as a Pizzeria in Torrejon de Ardoz - he was there in '60 & '61. Later he moved 'uptown' and opened a Pizzeria, later a full service Italian restaurant on the square across from Estadio Bernabeu (in the 1970's). It was on the south side of the square. I don't know if he's still there.
La Beata 'rings a bell:' a mesón across the square from a Church known by that same name but in Sevilla rather than in Madrid. Maybe there's one in Madrid, too.
BTW
Your profile says you're a telecom analyst. Were you at the Eircom conference in Ennis, County Clare (Temple Gate Hotel) on 29 & 30 September? I happened to be staying at the Temple Gate that weekend so I visited the exhibition (Preacher's Pub at the hotel and, of course Cruise's Pub).