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If you leave the transit area, you will have to pay $ 18 Airport Tax. It is not included.
As to Buenos Aires... its one of the world;s great cities. Very European style, high quality food and shopping. As waht to do. Go to Plaza St Martin. Airport bus every 30 minutes to small bus terminal near Sheraton Hotel at Plaza St Martin. When you get hungry ask go to Restaurant Establo ( Rua Paraguay ) ask taxi drive if needed. Even taking a taxi will be no more than $ 1.50. Eat their huge(600+ gram) Bife Churizo for about $ 9 and good Malbec $ 10-16 per full bottle. Though an Irishman would like that. Say hello to my favorite waiter Jorge from >Mara Brasiliera Senor Gringo from New York<

You can take public bus from outside terminal to downtown for less than $ 1. Takes 90+ minutes though but you see the neighborhoods on the way.
Bus 82 ( I believe but re-check ) walk straigh accros parking area after exiting terminal, bear to the left about 75 meters and you will see the public bus stopn). You could always take bus into city and then airport bus back ( from behind Sheraton Hotel ( $ 12 ) every 30 minutes on the full hour and the Half hour. Small terminal for only airport busses. Do not go to BA main bus terminal. tHave fun. You might just fall in love with that city. If you change your mind and want to stay a little longer I know a very ceap hotel ( $ 22 per night in the center.