A couple of things that I thought of, that come up again and again-
Towels- Argentine towels are tiny, thin, and scratchy.
If you like a big, soft luxurious bath towel, bring one along.
Cooking pots- obviously, if you dont cook, this is irrelevant- but if you do like cooking, it might make sense to throw in a pot and a frying pan- You can go to Macy's in any mall in the USA, and get a decent set of stainless pots and pans, or even Calphalon, for about what one good pot will set you back here, and, in a city of 4 million, there are seemingly only about two stores that sell really good cookware at all.
We bought a set on sale at Macy's for just over a hundred bucks, packed it in and around our clothes, and have not been sorry at all.
Similar situation with good chef's knives- they are half or a third the price in the USA, and easy to find, while in BA, good ones may exist, but it will take a couple days work to find one.
One thing to remember- Internet shopping doesnt really work in Argentina.
You can shop online for local stuff, at sites like Mercado Libre- but the entire concept of next day shipping of any consumer good known to man, at discount prices, that americans have come to take for granted- it aint happening here. Chances of a shipment from North America making it to you here, in less than a month, and with less than 100% markup for taxes, fees, and shipping, are negligible.
You cant just click on that buy it now button, and expect books, or cds, clothes, makeup, shoes, or any of the thousands of items you get that way in the USA.
On the other hand, there are thousands of cute neighborhood stores all over BA, with actual people who really know something about what they sell, and are generally very nice. I am on a very friendly basis with my local picture framer, watch repair guy, hardware store, plumbing supply store, and electrical supply store, I have a couple different barbers I go to depending on mood and hair length, I know my greengrocer and meat guy and ice cream purveyor, my local electronics repair man (which, of course, doesnt even exist in the USA as a job category). When my wife goes in the neighborhood coffee bar, they begin preparing her espresso, as they know what she wants.
I have a particular antique store for furniture, another for glass chandeliers from the 50's, someone who sells kitchen supplies, another for custom upholstery and drapes, and on and on.
Its like going back in time 50 years for someone who grew up in an America of 7-11's, Targets, and K-Marts.
Yes, there are Malls here- although they are as much for the social promenade as shopping. But the malls have edgy local designers selling wacky stuff, (Check out Jessica Trosman) right next to Zara-which, incidentally, is a good place for cheap basics- jeans, sweaters, and, yes, the elusive sock.
Malls here, though, are still novelties for the wealthy- everyday commerce occurs in small local stores. Which often have very different stock from each other, or cute new old stock from 20 years ago.