I've easily caught cabs from central Madrid to the airport for flights leaving at 7 am. I've stayed in Madrid about half a dozen times but probably don't know it as well as MADFlyer. MADFlyer - would another option for SeAAtle to stay in what I think is the Salamanca district, for example at the Hesperia Madrid, or the Miguel Angel Occidental. I seem to recall that these hotels were en route to the airport from the centre of town, but were closer to city sights than airport hotels.