I have a particular affection for Ezeiza because for me it is synonymous with Argentina and Buenos Aires. I do understand that this is completely subjective! My first contact with the customs officers, who are friendly and polite, often makes me think that human beings are much friendlier on this side of the Atlantic. I have already written about this on my Blog "Destino Buenos Aires".
To get into Buenos Aires you can take a taxi, or the Tienda Leon bus which takes you to the area of Retiro. From there one of their taxis can take you into the centre of the city.
During your stay in Argentina, if you want to fly to other towns in the province you need to go to Jorge Newbery, the domestic airport, which is right next to the Rio de la Plata in the centre of Buenos Aires. It takes one hour by taxi to get there from Ezeiza.