It is important to focus on a couple of neighborhoods if you are going to rent an apartment. That is what I did when I travelled to Argentina last year and was looking to get an apartments for rent in buenos aires. I decided that the best neighborhoods were Palermo and Recoleta because I had been told they were really safe and luxurious. I was right, and had the best time ever.
But, if you want a neighborhood with a little bit more of Tango tradition, you need to stay in places San Telmo like, La Boca or Abasto. Actually, Abasto was the place of birth of Carlos Gardel, the main Tango singer from all times.
So I hope this will be useful for Argentina travellers!
Lindsay