Daniele's apartment is a great option. It is located in a very convenient area, close to Atocha station and to many other interesting places such as restaurants, bars, museums. The apartment is very clean and organized. The bedroom and bathroom are very good - best bed and shower I have experienced at Airbnb.
Daniele is very easygoing, friendly. He will give you a list of excellent places to visit in Madrid, including tapas places and restaurants.