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Barajas is located 8 miles (13 km) northeast of the center of Madrid. There is a tourist information center is in the arrivals hall. If you read Spanish, access the airport's Web site, a work in-progress.
Taxis are available outside the arrivals hall. Fares are metered, but if the meter is not working make sure you agree on a fare before departing. The fare should be about 3,000 pesetas ($20) to the center, depending on the traffic, and the trip will take from 30 to 60 minutes.
An airport bus leaves every 15 minutes during peak travel times from 6 A.M. to 1 A.M., with less frequent departures during off-peak hours. The bus goes to the Plaza de Colon in the center of Madrid. There is a taxi stand at the Plaza, so you can take a taxi to your final destination. The bus fare is 300-400 pesetas ($2-$3), and travel time is 30 to 60 minutes, same as the taxi.
Rental cars are available from companies including Hertz, Avis and Atesa/National, but very expensive. It is much easier and more cost effective to take a taxi to all your destinations unless you are traveling outside the city.
World Airport Information Main Page
Adapted from How to Get Out of the Airport