I stayed in the Hostal Machin and absolutely loved it. It consists of about half a dozen rooms up on the 4th floor of a building on a street just off the Gran Via (so it's as about as central as it's possible to get but, because it's a fairly quiet street and so high up, there's no real noise problem).
There are shared bathrooms (unless you're in one of the one or two twin-bedded en-suite rooms) but I never saw anyone else using either of the ones close to my room and they were immaculately clean at all times (as was my bedroom). The bed was really comfy and the air-conditioning worked really well, as did the free wi-fi. The hotelier is really friendly and helpful. There are plenty of places nearby to get breakfast.
...and the really good news? It's only €22 per night (single) or €19 pppn (double or twin). I can't recommend it highly enough!
http://hostalmachin.com/ING/index.htm