We had a great stay at Jesus and Sara's Airbnb in Madrid. They were able to accommodate our very late (2am) arrival, and were in regular email contact to see if we needed anything. The place was very clean and comfortably set up. The Madrid maps and guidebooks were a nice touch. The building was nice and quiet, and the neighbours friendly.
Location is close to the very nice Retiro park and a few different metro stations but a little on the far side for walking to the centre of Madrid - we often walked one way and took the metro the other way.
Try the Museo Cerralbo - we enjoyed it more than the bigger museums. And skip the Temple of Debod; it was a real let-down.