This Madrid hotel is in the Salamanca district and the Diego De Leon metro station. The Trip Adviser reviews are excellent as well as the price. Is this too far from downtown to enjoy the sites?
You can take the subway from your location to anywhere you want to go The main destination would likely be Puerta del Sol, where you can walk to the Royal Palace, Plaza Mayor, the Cathedral Alumedena or in the opposite direction to the Park Retrio, City Hall, Prado...there are other stops closer to each of course, but the walks are part of the experience. The Salamanca District also has interesting sites to see....you would enjoy yourself there I am sure.