I have celiac disease and maintain a very strict GF diet.
In Argentina, gluten free is tagged as Sin TACC, which means without wheat, rye, barley and oats.
There is a huge variety of food and there are even a few gluten free restaurants that serve even pasta.
I am including one link and if you send me a PM I can give you some information.
I usually rent an apartment and go to Dietetica Viamonte and buy tons of stuff, empanadas, pizzas, pasta, breads and cookies/alfajores.
Every time I travel there, I bring back up 150 lbs of food back to the US. The prices are great and their products amazing.

http://argentinarocks.blogspot.com/2...nos-aires.html
http://www.almacel.com/saliracomer/verlugar.asp?catid=2
http://www.almacel.com/saliracomer/v...m=Restaurantes
http://www.almacel.com/saliracomer/v...m=Restaurantes
If you tell somebody at a restaurant that your are "celiaco" they will understand. Look for the head waiter or the owner and explain your situation. I found that in most places they understand.
I can eat french fries but sometimes they are fried with other things so depends on how sensitive you are.
Grilled meats are usually safe and even the chorizos/sausages are usually safe.
Breakfast is the hardest time for me. I would suggest going to the store, buying some great croissants and bread, bring some aluminum foil with you and take it to the restaurant for breakfast and tell them to warm it in the oven inside the aluminum foil.
Service is Argentina is superb. Some of the waiters have worked in the same place for ages and take pride in making sure your needs are met.
For dessert, flans are usually safe, most ice-cream is gluten free (Freddo - a large ice cream chain has some flavors that are certified gluten free while the others do not include any gluten ingredients) and try the Charlotte almendrado which is an ice cream cake (no cake) with almonds and chocolate.
There is even gluten free beer.
If you want I can send you some other gluten free sites. I am not sure if you speak spanish.