We will arrive in Madrid and depart as soon as possible for Cordoba. I see on the map that we can get to the Atocha metro station from the airport, but the Atocha train station is not the same. Are they connected the way some of the London tube and rail stations are? If not, is it feasible to walk on the sidewalk? Should we opt for a different method of getting to the train station from the airport?
As I recall, the Atocha metro stop is a fairly short block from the entrance to the AVE station. I would be hard pressed to imagine a faster, cheaper, more reliable way of getting from the airport to the station.
This website answers this question well.
http://www.travelinginspain.com/madrid_train_station.htm
Good luck!
I remember taking the metro in Madrid. There's metro stops, Atocha Renfe and Atocha. Metro stop "Atocha Renfe" stops inside the Atocha train station while metro stop "Atocha" stops outside the Atocha train station. If you happen to exit out of metro stop Atocha it spills into the streets where the famous museums are nearby and is a short distance to Atocha train station.
Hope that helps!