Well, despedida season starts in a few weeks - by which I mean the yearly expatsodus. Late April through mid-June you can usually find some good deals in the classified section here or from gringo amigos who fly the coop for warmer weather.
I love to shop at neighborhood furniture store, you can see everything from outside, and if you find one you like, try to negotiate with the owner. Argies do not like to give deals, but I always get a deal by buying 2/3 things, and they can deliver to your apartment in a few minutes, instant gratification. I also get to know the owner. This is the furniture that the owner has been collecting for a long time, some are used and get repaired and some are new. They usually look attractive and fit in apartment well. The ones you find at Ave Belgrano can be big that designed for houses.
If you want really cheap stuff go to the Salvation Army store in Pompeya.
http://ar.kekanto.com/biz/ejercito-de-salvacion
The Nº 28 bus goes right through Sat Telmo on Bolivar Street & stops in front of the store.
On the way back you can take the same bus. It goes through San Telmo by way of Peru St.
PM me if you need more info.