The apartment is close to the Atocha station (very convenient, if you have to catch a flight early in the morning ;-)). Nevertheless it was not too loud, and we slept very well. The apartment is well equipped and we found it clean and comfortable. We didn't mind climbing the stairs to the 4th floor, but it might be a problem with heavy luggage...
You can reach the city center within a short walk or with metro or bus, and Museum Reina Sofia is just across the street. Supermarkets, bakeries, restaurants, bars are all around, and Mercedes and Enrique have quite a long list with tipps!
We enjoyed our stay (3 nights) very much and will definitely consider to come again!