The budget is a serious consideration when you take a trip. Regardless of how much you're prepared to spend in Buenos Aires, there a few things you should be aware of when it comes to cash.
ATMs can be found in any bank, though there is usually a limit to how much you can withdraw -- I used several different ones and was always cut off at AR$1000 -- less than US$250. That doesn't last too long, and of course you have bank and ATM fees to be wary of.
Many places won't accept anything but cash. Some offer discounts if you pay in cash. Others have deals with banks in an effort to get people to pay with plastic, so you'll find some grocery stores and restaurants offer discounts to those who pay with a card from a certain bank. You can't go wrong with cash, though.
Change is chronically difficult to get. The largest bill in regular circulation is AR$100, which is worth about US$25 -- however, if you try to pay a 30-peso check, or even a 70-peso check, with a 100-peso bill, you will almost always be asked if you have something smaller. If you don't have exact change in coins and they don't have the coin power to give you, they will either give you those centavos in discount, suggest that they owe you and will pay you next time, or offer you a few candies or a lemon or something to make up the extra that you gave them. The small mom-and-pop type stores have a harder time with this than the bigger ones, but even in grocery stores sometimes you will have to wait for five minutes until the employee in charge of the change comes by your aisle with change for the checkout person. I tend to pay in 100s at the movie theatre and restaurants, and save my smaller bills for the verdulerias.
Speaking of smaller bills, you will want them for the taxis. Handing over $100 is a good way to screwed (the driver might say you only gave them a $50, or pull a quick switch and show you a fake $100, saying that that's the one you gave them). I don't mean to suggest that taxi drivers are dishonest -- the majority are good, hard-working people. But there are bad eggs who will take advantage of your foreign self. Beware, and use smaller bills.
Be on the lookout for fakes. There are several ways to tell: if you hold it up to the light, you should see the water marks. You can shine a black light on it to see tiny flecks shining back at you. There is a silver stripe that runs through the bill: tearing it just as the top of that stripe should reveal silver underneath. The numbers are ever-so-slightly raised (I don't like that test as I can't really feel the difference). And it's not just the 100s that are counterfeited -- I've seen fake 20s, as well. You'll notice that store clerks will habitually check the bills you hand them for authenticity.
Dollars are now a black-market luxury, so take care in how many pesos you withdraw -- changing them back to dollars here will mean a big loss for you. Don't try to take them back to States and exchange them there, either: I've heard that there are no banks in the US that will buy Argentine pesos right now. Check with your bank before you leave to be sure -- this is the type of situation that can change overnight.
And, as in any city, carry only what you need and be wary of pickpockets. As the economic climate wavers, we are seeing more and more of that sort of crime.