Hostal Oriente 

This was one of the most inexpensive places I found that looked nice and was in the area I wanted. I booked an individual room for 5 nights. It is easy to arrive at the hotel from the airport or train station by taking the Cercanias train to Sol and then walking about 10 minutes along flat ground. If coming by metro, the Opera stop is directly across the street. There was a large sign with the hotel's name on it, and then you press the buzzer to gain entrance. The first room I was given was not what I expected, and I actually went back and looked at pictures to see if I had booked where I thought. The first room was extremely small, and the bathroom was very outdated. Super small stall shower which leaked. I was not very happy, so I asked at reception if there were other rooms that had been renovated. There were, and I would be able to change the next day. I packed my suitcase the following morning, and when I came back in the evening, my stuff was in my new renovated room, which was MUCH MUCH BETTER! The new one had a larger closet with room to place my suitcase. It also had a bigger bathroom with a full-size shower and updated fixtures. Both rooms had a large window and a desk. Both rooms faced inwards (into the center of the building, not to the street) and were very quiet! Both rooms also had comfortable beds, safes, and hair dryers. I was surprised to see that reception is staffed 24 hours. They were helpful with storing items in the refrigerator, doing my laundry, and also allowing me to extend my stay after an unexpected flight cancellation. I have been to Madrid many times and almost always stay in this general area. I like having easy access to Cercanias and metro, as well as millions of stores, restaurants, bars, and sites. There were 3 options for breakfast within a 30-second walk - stores as close as next door - sites within 5 minutes. Once I got into the renovated room, I was very happy with my choice to stay here.