It depends on what you like.
The really cheap stuff is on sale in Once; often fashionable, but the quality is dubious to say the least.
Malls feature mid-market and top-end stores. Your best bets are Abasto, Alto Palermo and Patio Bullrich. Skip Gallerias Pacifico; extremely touristy and way more expensive than the ones further afield. Florida street is good for leather, though.
San Telmo has a very nice designer circuit, where the up-and-coming names of Argentine fashion sell their creations. Prices are high, but still a lot lower than in the northern hemisphere. Designer shops can also be found in Palermo, but those are generally much more expensive.
If you like to browse, Santa Fe avenue (roughly the first 40 blocks) and Cordoba avenue (blocks 20-60) are the main shopping drags.