We stayed here for 2 nights recently. It's at Calle de leon 13, 2nd floor (nearest metro, Anton Martin but also quite close to Sevilla). The QDQ website seems to have difficulty with this street, but you can get a picture by going to C. lope de vega 1 and then going opposite.
Its good points are: quite cheap (42.80 E incl tax for probably an average-sized twin room with private bathroom and balcony and TV); the bathroom as well as the bedroom had its own balcony (but the only one in the hostal to have this I think); plants on the balconies; clean; quite a good location (in Huertas) for access to museums, Sol etc; quite nice decor (cpmpared to some of the pictures on this website); quite a quiet street (sometimes); relatively attractive exterior, over a pharmacy with painted tiles on the outside; seems to be a 'safe' area.
Bad points: the room was meant to have air conditioning, but not sure if it did (there were air vents in the walls, but we didn't manage to discover how it works - which may be our failing!); because of the tall buildings and narrow streets, any noise in the street (eg even people talking) tends to echo, so leaving the windows open at night's not so good (especially when there are rubbish collections at 1am and deliveries of building materials at 7 am); c. leon can get full of a long traffic jam at times: this decreases traffic noise (less acceleration), but this is replaced by constant hooting; no supermarket very close: the nearest were at Sol (el cortes ingles); c de toledo (champion) and I think there's a Dia on C Atocha or c. magdelena; a really small bath (more like a deep shower tray really)
I think noise and building work is probably a feature of any street in central Madrid, so I'd be quite happy to stay in this hostal again, although I'd probably choose to stay nearer a supermarket.
Booking ahead is a bit tricky as there's no website, fax or e-mail, and not all the staff speak English. So you have to phone (91 429 51 37) or write a letter (which they will reply to, but not more than a month ahead of when you want to stay). Communications improved when I discovered that we all speak French! The staff are pleasant and helpful (we left our luggage there for half a day after checking out), although we didn't see much of them: I guess they were there if you needed anything, but you get your own keys, so they don't need to hang around the reception.