Oh, I totally recognize this! I was there once a long time ago with some friends and I remember how much I liked the area. However, I wasn't paying attention to where we went and since then I couldn't remember that neighborhood. I looked at my notes from that trip after seeing your photo, and now I remember we had gone to El Bonanno which is right there, too.

MM's directions from Plaza Mayor were very helpful. I might add that the Puerta Cerrada exit is the southwest corner of the Plaza Mayor, where you exit to go to Calle de los Cuchilleros (the street where the famous Botin restaurant is located). Calle de los Cuchilleros becomes Calle Cava Baja and then follow it to the end as MadridMan says.

Looks great!