I have stayed several times at the Hostal Bruna (sorry, I can't find the tilde). It is in a terrific location, right off the Paseo del Prado, across the street from the Prado museum and close to lots of great restaurants, cafes, plazas, etc. I have always asked for and received interior rooms, so there is absolutely no noise. Singles are listed on their website as 40E
http://www.ctv.es/hostalbruna/ but my son has booked them several times through hostelworld.com and has gotten a much better price.
I always plug this hostel when I can because of what I think was some pretty amazing treatment they gave my son last August. He was robbed late at night, leaving for the US the next day. No credit card, no cash, no nothing except luckily his passport. They calmed him down, gave him money to get to the airport and told him to send the money for the room. Highly recommended.
Laurie