In the interest of giving you useful things to do in Buenos Aires and information that will help you navigate the waters of this fair city, it seems super important to know where to shop in Buenos Aires and what to shop for.
1. Go leather shopping in Buenos Aires. Why? It’s simply awesome, especially if you go to Calle Murillo (pronounced “moo-ree-show”) near where it intersects Av. Scalibrini Ortiz. This is near the B line subway stop called Malabia (which is actually another street that is one block from Scalibrini Ortiz. This is not a frequented area by tourists in Buenos Aires at all, so very little English will be spoken. But oh man! You can get goat leather, rabbit leather, carpincho leather (carpincho leather is *amazing*), and of course cow leather. This is where all the “fabricas” (factories) are so you can get every type of leather and every item as well. Leather boots, leather gloves, leather wallets, etc.
2. Do NOT do any purchasing on calle Florida in microcentro. This street is somewhere you should definitely visit, but the reason to go here is people watching and window shopping. Florida street in downtown Buenos Aires is probably the worst place to shop in the whole country.
3. Similarly, do NOT go shopping at Patio Bullrich or really anywhere in Recoleta. It is simply overpriced and not worth it. You will not find too much that is authetically Argentine either.
4. Go to the Ferias Artesanales of Buenos Aires. There are many ferias and they are mostly on weekends. The most famous ones are the Feria de Mataderos and the San Telmo Antique Fair.
5. Do not plan on buying any electronics in Argentina. Anything electronic (laptop, phone, tablet, camera, etc) is going to cost 2 to 3 times as much in Argentina as it does in the USA.
Two more areas to check out would be Palermo Soho for the boutique clothing shops. They are basically all located between Plaza Serrano and Plaza Armenia.
You can also check out the Puerto de Frutos in Tigre if you want to go see what the suburbs of Buenos Aires look like. They have mostly things for the home (tables, chairs, plants, plates, etc) but they also have a lot of leather goods.