There's a place called GoFix (www.GoFix.com.ar) that has at least a few locations in BA, for apple products. I know of one on Juncal, right near the intersection of Uruguay, in Recoleta and I think there's one at least in Palermo as well. They seem to be pretty official places. Their website says they fix iPods too.
I went by there about a month ago to see about getting a screen replaced and they seemed very professional. I haven't used them yet, although I will be soon - my sister-in-law dropped her iPhone while visiting her parents and cracked the screen a little(second time it's been cracked).
I'd be careful about just whoever fixing these things. A friend of my sister-in-laws had broken her screen about a year ago and we took it to a place on Lavalle near 9 de Julio. It was cheaper than other places (like GoFix), but it was a little hole-in-the-wall kind of place. About a week after the replacement was done, she realized that there was a band near the top of the screen that would no longer read her touch. GoFix said the problem was either poor installation or a sub-standard screen.