Apartments

It's very easy to get a temporary apartment in Buenos Aires, they all more or less cost the same aswell, but what you should do is a lot of research about them, because you can get a really cool one for the same price as a really, really bad one. About the areas, they are more or less the same to be honest. But for some reason most people usually prefer the more clean areas of:
Palermo or Barrio Norte, but they are to be honest quite boring and expensive.

San Telmo is ok, allot of Tango places and bars, which are extremely hard to go by here.
Just do a quick search for it in google and you'll find plenty.
Whats good with San Telmo is is also that it is close to La Bocca, de facto, its just a ten minute walk...or 30. Depending how fast you are.

If you are gonna stay here for a longer period of time on a tight budget, have a look at
easyroomates.com , there you can find rooms for a more humane budget. ( 250 - 500 ARS 'a month ) instead of the whooping 1100 - 1500 ARS for a temporary apartment.
You can forget to get a real place to live as a pale none-Argentinian, sure, give it a go, but you are doomed and will only face degradation and mockery.