If you're traveling to Argentina on a tight budget, be sure to travel there in the low season months: March-June and September-November. Once you are there, head to buffet restaurants (called tenedor libre) and don't be overcharged. Always pay in the local currency, not in dollars.
The biggest saving you can definitely have is getting a cheap flight to Argentina. Also, travel as much as you can by bus in Argentina , which not only are cheaper but also very comfortable with plenty of leg room, nice meal services, free wine, etc.
Not long ago, a good way to save money was exchanging your dollars in the so-called blue market. Back then, you could get 10 pesos per $1 but currently, the official rate is $1 gives you 9.19 pesos, so you no longer can save this way, unless you do it in the dodgy white market.