There's just one place I've stayed which had a terrace big enough to have breakfast on - but that was in the Eixample neighborhood in Barcelona and it was a glass-enclosed terrace. Beautiful place, but that won't help you in Madrid.

While it's true there are a lot of flats - and even rental apartments - in Madrid which have balconies, they're usually not big enough to put a chair on. Anything more would likely cost much more.

Saludos, MadridMan