I heartly recommend La Morada del Gato, a just renovated apartment in a lively neighborhood, near to the undeground stations and the city centre. The owner took care of us with suggestions and exquisite hospitality (even a little present for my fiancée's birthday!). La Morada del Gato has everything you wish for a confortable stay in Madrid: warmth, elegance, care of details. In case you have any mobility problems, just take care that the house has no elevator, as the owner tells in the apartment's description.