I had a pleasant stay at Carmen's place. Her cats are extremely friendly, and Carmen does her best to help one with whatever questions one has about their stay in Madrid. There is a little walking to get from the train station to her place (about 8-10 minutes depending on your speed of walking), and it does take a moment to understand which street to walk up from the train station initially, but otherwise the location is good for your visit to the city, with nearby bus stops and metro line. You can get to the airport from one of the bus stops just outside the 'Atocha Renfe' train station - look for a line of people with suitcases waiting at a bus stop for the aeropuerto express 'yellow bus'.
Muchas gracias, Carmen!