One of my sisters did two tours in Afghanistan and my other sister did one tour in Iraq. I just wanted to say thank you!
Now, with respect to your budget, maybe it would help if I gave you info about ours and how much we spend etc.
We live in Caballito - it's not that close to Palermo but a 20 min subte ride will get you to Centro. We pay $2850 pesos rent plus $1200 pesos for expenses - granted we have a two bedroom apartment with a cochera. If we go out to dinner, we can look to be spending anywhere from $150 to $375 pesos for the two of us - including shared appetizer, bottle of wine, dinner and shared dessert. If you don't go out for sushi, you can expect to spend about that much (speaking of sushi - tuna here is usually from the can but the salmon is generally okay). Going to the supermarket and shopping for food for about a week and a half runs us about $500 - $700 pesos but we are two, I buy a lot of cleaning supplies for laundry (dry cleaning is expensive here) and I also buy dog food. So maybe you would be looking to spend closer to $300 pesos a week on groceries. If I were to take a taxi from Congresso to Caballito I am looking to spend about $30 pesos - depending on traffic of course. A subte ride is cheap - 1.10 pesos and buses cost around 1.25 (depending on the line and where you need to go). Also, we pay for private insurance - about $500 pesos a month (each).
Best of luck! Also - you are going to be hearing "vos" down here ;o)