We spoke to a few locals and they all said that El Cuartito is the place to go for pizza in Buenos Aires. Being from New York, we were looking forward to trying a local pizza, and must say that while different, the pizza at El Cuartito was pretty delicious. Others have spoken about the pizza itself so I won't go into detail, although I will note that the pizza is pretty filling, as this would be our last meal for quite some time (we ended up not eating for hours during our horrible experience with Conexionbaires.com [NEVER USED THEM]), and the fullness lasted.
Some advise for those of you who do not speak great Spanish (the staff doesn't speak great English) - when you go in, there is a dining room on the right. If you sit down there is waiter service. If you just go up to the counter (like this guy did) and order, they will give you food, but then if you go and sit in the waiter service area things get very confusing.
This review is the subjective opinion of a TripAdvisor member and not of TripAdvisor LLC.