Sara, look at Craigslist - that´s the "go to" spot for room rentals.
I just did this whole process over the past 2 weeks, I looked at studios, 1 bedroom and room rentals in a bunch of neighborhoods (San Telmo, Almagro, Abasto, Palermo, Las Cañitas, Centro, etc).
Private bedrooms in big shared houses with lots of travelers / spanish-school students can found in San Telmo for USD 350 a month but (in my opinion) they are aren´t the nicest places -- grimy, dirty kitchens, no air conditioning, crappy foam mattresses, etc. The cheapest places are mostly in San Telmo. For 400 USD + you can find places in Palermo or Barrio Norte / Recoleta. Rooms in brand new buildings with pools and amentities can go as high as USD 600.
Note that starting in February a lot of students (especially foreign exchange people) arrive in BA and start looking so if you are coming in a week you will still have a lot of options but if you stay in a hostel for a month and then start looking you will have less choice.
After running all over the city looking at places I decided on a studio because it was not that much more expensive than renting a nice room (room was 475).
Good luck!!
