Qualifications: i'm a cook in nyc who well researched her trip to explore a variety of food experiences. Firstly, I'd suggest you buy a wonderful little book, "The Authentic Bars, Cafes, and Restaurants of Buenos Aires" by Gabriela Kogan which steered me to the most interesting places off the beaten path, more a culinary history of the people's eateries than a Zagat guide. Here's an entirely personal list with commentary/locations:
Parrillas (mostly red meat grills that run from over-priced tourist halls to whole-in-the wall neighborhood joints):
Classic Don Julio, delivers the best cuts perfectly grilled to order along with beautiful salads and the freshest fries; great selection of Malbecs. Guatemala 4691 (Palermo Soho)
Hot, lively Cabras is a favorite of the locals, especially on Sunday brunch when everybody & his family chews the fat; cheap & fun - go for the mixed grill/share. Fitzroy (Palermo Hollywood)
North Argentine native:
Tiny La Cocina limits itself to the best, most authentic empanadas & locro in town; inexpensive, tasty takeaways; Calle Florida 142 (Microcentro) & Ave. Pueyrredon 1508 (Barrio Norte)
Newest Culinary sensation:
Tegui (several town chefs highly recommended) owned by an auteur cuisinier (which means he directs everything: from the tranquil California setting to the pristine kitchen); nouvelle cuisine takes on classic Argentine dishes; costly but worth it (about $US 50 for lunch). Costa Rica 5852 (Palermo Hollywood)
just-opened Italian cafe Arkakao for the most flavorful true gelato, perfect coffee/pastries, & best of all, an elegant & delicious hot/cold buffet for lunch (didn't eat anything until the day after), a bargain at $US 12. Quintana 188 (Recoleta)
La Boca Bodegas:
Rowdy but genuine El Obrero, a joint for true parrillo enjoyed by portenos who cherish futbol & assorted cuts. Good value; go with a group. Agustin Caffarena 64
El Federal, atmospheric cafe in San Telmo, exudes the intellectual/tango history of the city, offers the usual & nice toasted sandwiches. Carlos Calvi 399 (San Telmo) and Cafe Margot, lovely hangout for the stars of yesteryear's tango; some lovely dishes. Ave. Boedo 857 (Boedo)
avoid the tango shows & go for the real deal, milongas at Confiteria Ideal on Sunday afternoons. Born at the height of the tango nadir, 1912, it's more decrepit now, but where dancers tangoing all their lives carry on this great tradition of elegant coupling. sample the pastries with tea. Suipacha 380 (Corrientes).
City Food Market:
San Telmo Market offers lovely fresh fruits, vegetables, meats, dried fruits/nuts along with flea market goodies. nearby fresh pasta shops selling everything for an Italian repast
Avoid: Cafe Tortoni with its long line of tourists; ditto for over-priced, crowded Cabrera with its stale menu!