Hi Shazz!
Try doing a 'search' in hostels & other lodgings for hostal playa, you'll find a lot. I stayed there last year and this is what I had to say about it in my post:
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We stayed in Madrid at the Hostal Playa, and I would recommend it to anyone looking for a simple, clean, and affordable lodging. It's located just off Puerta del Sol, on Calle de la Victoria, literally a 2 minute walk to the Sol Metro stop. The owner was very nice, the room was clean, we had no problems. The room we had, though, seemed to be one of the not as nice ones, the furnishings looked older than some of the ones we peaked in that were down the hallway, and also when people came in late or early & made a lot of noise, we heard them. Our window also overlooked a 'courtyard' in between other buildings, which can also get loud if your window is open. Despite what this may sound like, it wasn't bad at all, and I would DEFINITELY recommend this to anyone. We had our own bath & tv and there was a table & chairs in there too. We paid 6,500 ptas for this double.
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We enjoyed our time there, and were there on a Sat & Sun night. It could get a little loud if the windows are open, but if you're going in the winter, you shouldn't have a problem with that.
Have a great time!
-GG
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"Vivir con miedo es como vivir a medias."