Take the subway from the airport to the Plaza del Sol stop and catch the double decker sightseeing bus. You get an all day ticket and can get on and off when/wherever you want. There are two routes. Take them both and then go back to the places you want to see in more detail.
Peaceable Projects Inc. is a U.S.-based non-profit group that brings the vast resources of the wide world together with the ongoing needs of the people who live, work, and travel on the Camino de Santiago pilgrim trail network in Spain.