I had the pleasure of staying for 1 month in Graciela & Paula's apartment in Palermo. For me, it was the perfect situation to experience everything that Buenos Aires has to offer.
In terms of location, it's only about 2 blocks away from one of the main subway lines that will take you to the majority of neighborhoods in the city. In addition, it is close to a shopping mall that has a variety of eateries for when you don't feel like wandering too far from home. Lastly, and perhaps most importantly, the apartment is just far enough off the main strip of restaurants and nightlife that Palermo has to offer that you can still fall asleep without hardly any street noise at all. At the same time, whenever you are ready for a night out on the town, everything (and I mean everything) in Palermo is within walking distance.
For myself, this trip was part-business part-pleasure, so it was important to me that there be good working internet in the apartment. I never had any issue with the internet in the entire month that I was there. Emails and internet searching worked very quickly, and any of the wi-fi calls I needed to make back to the states were clear and without interruption. In addition, there is a little balcony at the end of the apartment which is ideal to put your laptop and have a cup of coffee/tea while you enjoy the peacefulness of the street below.
Lastly, organizing the trip with Graciela and Paula was a breeze. They responded quickly to any questions/concerns I had prior to my arrival. They were always on time whenever we arranged to meet (both arriving at and leaving the apartment). Due to my longer stay, they were willing to change the sheets and towels upon request, which saved me from having to find a local laundromat. And lastly, since my departure flight was later in the day, I was able to make use of the apartment until well into the afternoon, even though the check out was technically at 11am (I'm sure this last point is not offered to everyone, but perhaps the apartment had not been re-rented yet and, as such, Graciela and Paula were kind enough to let me stay a few hours longer).
Overall, I couldn't recommend the apartment and Graciela/Paula more. If you are coming to Buenos Aires for anywhere from a few days up to a month or longer, I think you will be well satisfied with your time in this charming Palermo apartment.