As a tourist, you have more restaurants available to you than you can possibly visit during your stay. You will have the parrillas (grills) that you need to visit; your empanada place; your ice cream place; your craft beer place; etc.
But if you want to go to a local, family-run bodegon, then you should add this place to your short list. Ojo (Mind you), you need to make reservations because this place is always full... always! And if you do go, you just can't miss out on the following dish.
Pollo a la Gasparini
But before we get to the chicken, you absolutely have to do the following or the timing will be all off. I recommend you make your reservation for 8pm, before the crowds get there. As soon as you sit down, tell the waiter that you're going to order the chicken. If it's going to be at least three of you, with good appetites, then you should order a whole chicken and ask for extra fries, always ask for extra fries no matter how much chicken you order. Tell your waiter to go put that order in and to come back to get the rest of the order. I swear, I do this all the time.
When the waiter comes back for the rest of your order, you should order some pizza or some other quick appetizer. The chicken takes 45 minutes!
As far as pizzas go, it's not going to knock your socks off, but it's consistently good local thin pizza. I took this picture back in 2007 because it's been forever since I have thought to take pictures of their pizza.
Now, the chicken arrives. This is a braised chicken in white wine with lots of garlic, and rosemary. The fries are there to soak up some of that sauce!
This is one of my favorite local dishes. If I were to ever leave Buenos Aires, this would be one of those things I would miss.
Keep in mind that the restaurant isn't aesthetically pleasing. It's a large, well-lit, noisy hall with plastic plants all over the walls. The family runs the cash register and if you show up at 8pm, they will most likely be having their own dinner at the table by the cash register to take advantage of the calm before the nightly storm.
You will literally be eating amongst locals, soaking in that local culture like the fries soaking in that white wine sauce in the pan. If at any point during dinner you start to hear people singing, it's probably a birthday and it's customary for the whole restaurant to join in on the birthday song.
And if you can't make it to Argentina anytime soon, I found a recipe on-line that is pretty close, but you would just need to use rosemary instead of the thyme.