My brother and I had a lovely stay at the Persia room in Casa de Madrid. The place is easily accessible from the airport, just two train rides and a short walk (costs a little bit over EUR 3 per person). Felipe is a great host, he will provide all the necessary instructions to get to the place and answer questions/provide recommendations in the area. He is responsive and makes sure the guests feel welcome. I will definitely stay here again next time I visit Madrid, perhaps check out a different room at Casa de Madrid.