This weekly market takes place every Sunday in San Telmo. The market runs the lengh of Calle Defensa, starting at Plaza de Mayo and going for more than ten blocks.
I recommend starting your day in Plaza de Mayo and working your way south to Plaza Dorrego.
Along the way you'll see beautiful churches, street performers, and shop til you drop. Literally, you'll be shuffling slowly along with the crowds so wear comfortable shoes. Between the cobblestone and slow pace you'll be happy for supportive sneakers.
The market is cancelled for rain (it IS outdoors) and is only on Sundays. It says it starts at 10 am but not all vendors will be set up so early, I recommend a later start at around noon at the earliest.
Bartering tip: Don't do it. The prices are set fairly and this is not the market to barter in like in other countries. If you buy more than one item you CAN ask if they'll make a better price. Likely they'll just round down but don't expect them to slice the price in half.