Buenos Aires has some of the consistently best food of anywhere I have been in the world. Many of the restaurants serve similar fare but it is all very good and incredibly cheap to anything you are used to at home. You will eat like a king in this city every meal you want and spend probably around the same amount of money you would eating at home.
Most of the people that live in Buenos Aires came from European families, many of whom were Italian and Spanish. Apparently a ton of Italians came over during World War II and brought their cuisine with them resulting in what is some of the best Italian food outside of Italy. Many restaurants will designate at least one page of their menu to Italian fair offering fresh and homemade pastas, gnocchis, pizza etc. Veal milanese, scallopini, and caprese salads (fresh bufalo mozzarella and tomatoes with basil oil and vinegar) can be found on nearly every menu. Most restaurants also serve very good bread. Although they often do not have oil and vinegar on the table they are used to people requesting it and have it available (oliva y aceito...butter is mantequilla)
The other half of the menu at most Buenos Aires restaurants usually consists of beef. If I remember correctly Buenos Aires has one of the highest meat consumption rates in the world and beef is a dominating force on many menus. To the benefit of Americans it is VERY cheap and you will be baffled by how little a steak will cost you here and how many varieties will be available on most menus. There are parillas everywhere which is the Argentinean version of barbeque. Many parillas will have the grill and/or spit in plain view of the diners. The beef here is cheap and delicious. Cattle in Argentina are not generally stuffed into feedhouses and injected with a bunch of garbage like they are in the states. The cattle feed on grass and generally roam free as far as I understand from talking with people and you can definately taste the difference in quality and flavor of the meat. Parillas also often have an interesting way of offering salads which I found both convenient and smart. Instead of having four or five varieties like many places in the states they literally have a list of all the ingredients available and you simply tell them what you want. I don't know why no one at home has thought of this except at a buffet...
Buenos Aires is also famous for its gelato. Another treat the Italian immigrants brought over with them. Unlike gelato places in the states that never quite seem to be up to par with those in Italy, here they got it right. The gelato in BA is light and creamy and everywhere. The largest chain is called Freddo and they have outposts essentially everywhere. If you spend a lond enough time in the city you will inevitably pass by a dozen of them.
Two other Argentine classics I would not want to forget to mention: Provoleta is essentially a block of provolone cheese that is grilled on the parilla. It is served warm with olive oil and some combo of spices that I was never really sure of. While I found it tasty I was a much bigger fan of mozzarella milanesa (like a giant mozzarella stick topped with marinara) Also not to be missed is Quilmes beer, which is EVERYWHERE. If you think Bud or Coors has a stronghold on the American market wait until you see the domination of Quilmes in Argentina. It is cheap, light and good. A large bottle runs a couple of dollars and pitchers in bars are probably about three bucks.
While these are some of the best known items in Argentina all varieties of food are easily available. We actually went to a Japanese restaurant one evening that had excellent sushi. You really can't go wrong with food in Argentina. Everything is delicious and everything is safe to eat unlike many other places throughout South America. No risk to eating foods here so enjoy as much as possible!