I read about Pension Arcos in Rick Steves' guidebook and I LOVED it. A small double room with a full en suite bath was only 40€ per night, and it is seriously no more than a 5 minute walk to Puerta del Sol, the CENTER of Madrid. However, if you are looking for luxury DO NOT STAY HERE! If you want inexpensive, safe and, well, quaint, this place is a bonanza.
Anuncia and Sabino (proprietors) speak no English- you'll need your Spanish in order to reserve a room- no more than the day before your arrival. It's on the top floor of a building that has been given over almost entirely to hosteles/pensiones- but there is a charming, antique (small but powerful) elevator. When you walk in to the place, it is almost like stepping in to your Aunty's or Grandmother's place- NOTHING is new, but it is all clean and well maintained.
Anuncia made sure that we knew where we were headed- took us through the lounge area out to the terrace and pointed out the street we needed in order to reach our destination. That terrace alone would be worth 40€ during the warmer months of the year!
My ONLY complaint is that, when we returned to the room to study for the finals we had to take when we returned to Barcelona after a day out visiting museums, eating AWESOME food and flirting with CUTE Madrid police officers, it was COLD. So cold that we hunkered down under the bevy of blankets on our beds. We cranked the dial on the old radiator, to little effect, but when we returned from dinner, it had warmed up enough to be comfortable in street clothes. Full disclosure: I don't do well in the cold. I live on Maui and am currently attending school in Barcelona which is a good 20°F warmer than Madrid.
If you are a Rick Steves' devotee, you will ADORE this place- and Anuncia is a huge fan of Rick and the people that have come to her through his recommendations.