In reply to Sam Dragoman:
There are plenty of places. The older traditional place is Orviz:
http://www.orviz.com/ but others are good too. There are several lesser places along Ave Las Heras - it runs perp to the main ave (San Martin) in the city centre and turns into Ave Juan B Justo where Orviz is.
Also along the main pedestrian mall, Paseo Sarmiento, there are several gear shops that mostly sell, but also rent gear. Plastic boots, crampons and axes are all no problem, but you may end up having to buy some clothing. The stuff there is good quality, not as cheap as it should be in those shops, but OK. A bit out of the way, but good, is:
http://www.chamonix-outdoor.com.ar/