This neighborhood is home to the hostel I have been living in for the past two months. It is also financial district, meaning it is filled with businesses and thus, thriving during the week, but quiet on the weekends. It is also filled with tons of great cafes and restaurants, and is where Puerto Madero and the nature reserve are.
San Telmo is my favorite neighborhood. It has La Casa Rosada and a number of other historical landmarks and museums, a Sunday feria filled with amazingly talented local merchants, and some of my favorite restaurants, which, along with other places in this neighborhood, are open on the weekend.
Home to the famous cemetery, Recoleta is always bustling. While I have not spent a lot of time there, I know it has a number of great cafes, a fabulous movie theater, and a great feria on both Saturday and Sunday.
Palermo is known as the place to be. It is great for nightlife due to its number of clubs and bars, has a ton of places to shop, and its own feria in the center of a great shopping area that, like the one in Recoleta, is also open on Saturday and Sunday. I have only been to Palermo a few times, but I really enjoy it. It has numerous beautiful parks and great cafes. I definitely wish I had spent more of my time there while in Buenos Aires.
Definitely visit La Boca while in Argentina. It is a big tourist attraction and very worth seeing. It is filled with bright colored buildings, Tango shows, a feria, and much more. It is something you can do in one day, but it is not the best neighborhood to visit so it is important to only go during the day and not stay after dark.
I have only been to Retiro once so there is not much I have to say about it, but I know there is feria there on both Saturday and Sunday and it is home to the train and bus stations, which you will need if you plan to travel outside of Buenos Aires.
Again, these are not all of the neighborhoods in Buenos Aires, just the ones that I have visited and wanted to discuss. I highly recommend visiting these neighborhoods during your time here and taking your own time to do you own exploring!