Hi mahla,
I´d like to let you know that my sister is renting her Recoleta flat, I don´t know how familiar you are with Buenos Aires or its neighborhoods but her apartment is on Ayacucho and Posadas, right in the heart of Recoleta (widely considered as one of the best places to live in the city of Buenos Aires you can do research online or ask any locals about the area) the flat is right around the corner from the Alvear Palace Hotel and the Louis Vuitton store.
She actually owns it and usually rents it while away (so theres no contract, warranty fee´s, etc) She usually charges 350 U$ a week but you can always talk to her and negociate the price, dates and special arrangements if needed, please let me know if your interested as soon as possible and I will provide you with her contact info.
Best,
Fede