The apartment was nicely updated. It's located on the top floor (4th) in a historic building built in the 1800s. Thus there is no elevator so travel lightly. The stairs are not user friendly for large luggage.
It's walking distance from Atocha train station. In general, you are located within decent walking distance (15-45 mins) of most local attractions i.e. Plaza Mayor, Mercado de San Miguel, Royal Palace of Madrid, Templo de Debob, Puerta de Alcal, etc. We we're able to walk to all the major attractions with 1 1/2 days. The free walking tours also helped with that.
Fernando provided a local attractions map with hand written notes on where to go and what's in the general area. This not only helpful for picking attractions but even how to get back home when you have no data.