I offer a room in Lavapiés quarter. It's a picturesque and multicultural quarter in city center. You've 2 subway lines walking from the appat. Area plenty of bars and restaurants, you've pretty close Atocha Station, Reina Sofía Museum...among others.
Lavapies district, which used to be the core of jewish and morish life hundreds years ago, is definitely the most cosmopolitan zone in Madrid. Having been one of the most genuine zones in the capital …
You can get the subway lines 1 and 3 in less than 5 minutes walking.
Anyway the flat is so centrally located that you almost don't need to take the public transport.