If you're not vegetarian, you will want to try asado (beef/steak barbecue) at a parrilla, restaurants specializing in roasted meats. There are expensive parrillas, and more simple and cost effective ones, . The bife de lomo (tenderloin) is unbelievably tender in comparison to US beef and is more reminiscent of European cuts. Jugoso means rare (literally "juicy"), however the Argentine concept of rare is very different from that of someone from the States (perhaps its a tourist thing, but an American ordering rare is likely to get something between medium well and hockey puck).
Don't be afraid to order "azul" (blue), you will not get a blue steak, more like an American Medium Rare. If you like your meat bloody it might pay to learn words like "sangre" (blood), or to make statements like "me gusta sangre" (I like blood). Don't be afraid to spend two minutes stressing how rare you want your steak to your waiter- this is something no one talks about in guidebooks but every other American and Brit once you arrive will tell you the same thing.
Italian and Spanish food are almost native here, as the cultural heritage heralds in great part from these two countries. Other popular meals are pizzas and empanadas (small pastries stuffed with a combination of cheese and meats). They are a popular home delivery or takeaway/takeout option.
The pizza is excellent in Buenos Aires, due to the Italian immigrant heritage. Pizza comes al molde (cooked in a pan, usually medium to thick crust), a la piedra (baked in a stone oven, usually thin to medium crust), and a la parilla (cooked on a parilla grill, very thin, crispy crust).
One incredible and typical Argentinian kind of "cookie", is the alfajor , which consists of two round sweet biscuits joined together with a sweet jam, generally dulce de leche (milk jam, akin to caramel), covered with chocolate, meringue or something similarly sweet.
Service: do not expect service to be comprable to large cities in Europe or in the USA. Service in Buenos Aires can be slow at best and horrific at worst. Don't expect your waiter to take your drinks order when the menu is delivered and don't expect the menu to arrive quickly. If you want ice in your drink, expect the drink to arrive several minutes before the ice does.
Patience is the key. Argentinians as so accustomed to bad service that they don't bother to complain direclty to the waiter/waitress but moan amongst themselves. Speak out if you feel it is appropriate.
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