What to do in Buenos Aires on a Sunday? My recommendation is, to go to San Telmo! San Telmo is the oldest neighborhoods of Buenos Aires.
The main highlights of the neighborhood are the small, cobblestone streets and, among others, the beautiful colonial buildings, the market and the Plaza Dorrego. Here you can find many nice restaurants, bars and (backpackers) hostels.
There are many things to do during the day and in the evening. During the day, there is a nice souvenir fair at Plaza Dorrego that continues on into the nearby blocks.
In fact, there are so many stands that it is almost impossible to see everything in just one Sunday! There are many different stands with antiques, art, trinkets, tango and delicious food. If you are looking for a place to buy souvenirs, this is where you should go!
During the evenings, you can find artists and people playing music and dancing (tango) on the streets. The Plaza Dorrego is actually an outside milonga! There are many people dancing Tango and many people watching them. The atmosphere is absolutely amazing.
If you are hungry, I would recommend going to el Banco Rojo to get some food. It gets very busy but that is because the food is so delicious!
Another option is you bring your own food to Plaza Dorrego and enjoy the ambiance with a glass of Malbec while watching people dancing the beautiful Argentinean tango.
This is another perfect night in Buenos Aires.