Centro Pet, Cordoba 1475, phone 011 5365 6101
4th block west of 9 de Julio, between Uruguay and Paraná
I'm not saying it's the biggest, but I have seen hamster-cage-like objects in the window. Which, this being Argentina, doesn't guarantee they have them now, but it's a start. And their ad says they have stuff for rats. Also, apparently, a vet on premises.
To find a cage suitable for hamsters you need look no further than the government cabinet in Plaza de Mayo. There's one big hamster called Massa already turning endless circles in the cage with no easy exit. The bigger hamsters, some call them rats, have already been let out to play!