Don't miss Desnivel, in San Telmo...a raucous local joint serving up (what else?) every imaginable cut of beef on the parilla, with chimichurri and salsa on the side.  If you are a vegetarian, you might want to steer clear...

If you want to try empanadas, wine, great meat, alfajores and mate all at once, I recommend the The Argentine Experience. It's great for meeting people and since it's closed doors, you get a very cool service, they will teach you words and expressions... it's very fun. For local and cheap restaurants, I always recommend Sarkis (Armenian food -- for me, the BEST restaurant in BsAs by far, super cheap and delicious), Salgado (pasta), Miranda, La Cabrera, Las Cabras, La Dorita (meat, parrilla), Burger Joint (for an amazing burger and great service), Malvon, Oui Oui(brunch). All of them are either in Palermo or Villa Crespo (neighborhood walk from Palermo).

Hello, famous Aramburu Bis restaurant is a very good choice for anyone who is searching for good food. Also, try La Familia in Buenos Aires.

You can go to Las Cholas and La Colorada (Migueletes and Newbery) in Cañitas or Las Cabras in Palermo which are grill houses with some argentinian food like "humita", "pastel de carne" or "empanadas", they are charming and really cheap.

A friend of mine whose father is from BA and who goes there once a year told us about Freddy Restaurant Parrilla which is a little sandwich place by the San Telmo market. Crazy good, although totally unhealthy and I was a little skeptical about the cleanliness of it (it's basically just a little bodega-type place), but wow, would I go back in a minute! Great local find.