I visit BA 2-3x a year for business and will agree it is a fantastic place to visit! I usually stay in Recoleta, Palermo Hollywood or Puerto Madero. And note with three Pesos to the Dollar, the exchange rate is in your favor!
As others have said Argentine beef is the best and they have excellent wine (ensure to have a bottle of Malbec). No matter where you go, you will always find a great steak. However my preference is Spettus Steak House at Alicia Moreau de Justo 876. This restaurant stands out for the variety of dishes and the care in the preparation. Its strongest point is grilled meat, some of which is barbecued on a spit and offered to diners at their tables, at regular intervals. There is also a great selection of salads as well as seafood. It offers more than 20 different cuts of red meat, pork and chicken.
Mind you, be safe when you travel. Especially at night! Walk in well lit areas, walk amongst others and stay away from the train tracks. Speaking from experience, I have never had an incident and I've been fortunate to travel to a dozen countries, but I'm 6'5" and an ex-cop so I was quite surprised to have three kids try to rob me at knifepoint as I walked down Juan B Justo Avenue at 7pm, which is a main avenue in Palermo Hollywood. As always, be alert of your surroundings..