I wish I had known BEFORE I did the research and completed the two gallery walks outlined below that there is actually a website which maps out the contemporary art galleries in Madrid. It did not come up in a google search, and either the art group in InterNations Madrid did not know about it, or they decided it should remain a well-kept secret. Anyway, for next time (for example the gallery weekend in September, which unfortunately coincides with the Berlin Art Week), here it is, and the Facebook group is here.
My relatively short art walk on day 1 started in La Casa Encendida, Ronda Valencia 2, and continued to C/ Doctor Fourquet with six galleries in the numbers as follows: 5 – Joaquín García, 8 – Sin Fin, 9 – Juan Risso, 12 – Bacelos, 17 – Espacio Minimo, and 35 – Alegria. However, be aware that they have very limited, and very erratic opening hours. Heaven forbid that they attract visitors by coordinating their opening hours like galleries in the rest of the world logically do. Also, the numbering seems to be a complete mess. The walk ended in CaixaForum – a must visit, especially for the architecture.
Note to self: Many tapas restaurants in C/del Leon.