If you are in the southern side of the city, I recommend Hospital Britanico, I am paying about 550 a month (but it is always going up!) One thing I like is that they seem to put the money into machinery and doctors, and not making the hospital look like a hotel.
Also, most expats don´t like to do this, but keep in mind that if you have an emergency (or any non-emergency) any public hospital must admit you, for free. If you have a complicated surgery they might ask you to pay for supplies.
Some of the hospitals are pretty nasty looking, have long lines, but the actual doctors are the best in Argentina (a lot also have private practices) because they see a lot of cases and are chosen by "concurso".
My husband doens´t believe in private medicine and he is quite happy with the dental and medical care he gets at publich hospitals, though he does not like the effort in getting a "turno".