We had a great stay on Ari's apartment in Palermo. It's near the subway station and the neighbour is very interesting. It's very comfortable to stay for several days.
It's important to keep in mind that the kitchen and the room are practically the same thing and if you want to cook a lot it may not be the best place to stay.
But you shouldn't be cooking anyway, as you are supposed to enjoy Buenos Aires and try some of the great restaurants and cafe's that you have around the house and all over the city. Right? =)