Here are some of the most popular things to do while visiting Buenos Aires.
-San Telmo on a Sunday. The San Telmo market is a huge market through one of the streets most historic neighborhoods. There are hand-crafted arts and there is tons of street music. If you happen to be in Buenos Aires on a Sunday, you HAVE TO do this.
-Recoletta Cemetary. this is a cemetary that is filled with the graves of really rich people who´s familys built huge house-like structures and statues for their deceased relatives. Also where the body of Eva Peron is burried. if you are in Buenos Aires for more than 2 or 3 days, this is also a must do. (this is better to do on a saturday or sunday since there is also a market here on these days)
-Plaza de Mayo. This is a plaza that is located in the middle of downtown Buenos Aires. This is the most important spot in regards to the political history of Buenos Aires. The Pink House, Argentinia´s national capital building, is located here. In the 1960s Eva Peron gave her speeches from the balcony to screaming crowds who were standing in Plaza de Mayo, it is where people protested during the ¨dirty war¨ (Argentina´s genocide), it is where hundreds and hundreds of thousands of people met after the stock market crash of 2002. Check out Plaza de Mayo and do some reading about it beforehand. I would recomend checking out "My Buenos Aires Travel Guide", written by Sandra Gutrejde Suarez (included in my links section). She has an excellent blog post which describes the geography and history of Plaza de Mayo.
-the obelysk. At the intersection of 9 de julio (apparantly the widest street in the world) and Calleo there is a huge phalic obelysk that commemerates the first raising of the Argentinian flag. Its not that neat but you probably want to say that you saw it.
-Linea A of the subway system. Ride it somewhere. The subway line was made in the early 1900s and they still use the original cars that are all wooden and antique looking with swinging lamps and stuff. really cool. not alot of toursts ride the subway.
-the touristy and colorful part of la boca. this is a must. It is what Buenos Aires is most famous for (in a pop-cultural sort of way)
-Teatro Colon (Columbus Theatre). This is one of the best teatres in the world. There are shows all of the time and you can take a tour of it if you want to.
-MALBA (museaum of Latin American art). This museum has the best collecion of Latin American contemporary art in the world.
-Museau de Belles Artes- not an incredible collection but it is huge and it is free and it is right beside the Recoleta Cemetary
-Tigre. a small town only a 1 hour train ride out of Buenos Aires. It is a marsh city and nobody has cars. They all drive boats to their houses. There are also boat taxis that drive up and down the ¨roads¨.
Most importantly, geek out at Argentinas Travel Guide (argentinastravel.com). It has alot of information about things that are off the beaten path. it is written by expats living in Argentina. This is the best resource for Argentinian travel.