Buenos Aires suprisingly has great vegetarian restaurants and also many restarants cater for vegetarians. Most chinese and middle eastern restaurants have vegetarian options. Armenia Village in Palermo Soho has excellent restaurants.
These are my favourite vegetarians click on links.
Pericles' last link, to Casa Felix, is one of the best restaurants in Buenos Aires, although its not a restaurant at all.
Diego Felix cooks for a few people, in his house, and he is an incredible cook.
His main course is usually fish, no red meat, but the meals are 5 courses, and the other 4 are generally vegetarian, but, on request, he will do vegetarian or vegan meals.
100 pesos, and worth every penny. Anywhere in North America or Europe, a meal like this would cost $100 or 100 euros.
This is a world class chef, cooking in an intimate setting, and explaining each dish to you, and is one of the best meals you will ever eat.
There's a great Chinese-run tenedor libre veggie restaurant on Calle Belgrano in Once. It's called the Golden Fenix (I think they have a website).
Get there early for the freshest veggies and soy dishes.
Bio has some tasty dishes, but you might not want to eat there every week because they are a bit pricey. They have a lot of vegetarian choices and their food is all organanic. Their website is http://www.biorestaurant.com.ar
I would highly recommend Spring in Palermo Soho, at Borges and Charcas. It is a tenedor libre with a large, fresh selection of all vegetarian options and only 23 pesos for lunch and 26 for dinner M-F, a few more on weekends: http://www.springrestaurante.com.ar/
Check out The Natural Deli in Las Canitas. It's not a vegetarian restaurant, per say, but they seem to have a lot of veggie dishes and serve organic foods. They have smoothies! They also have a shop in back. http://www.natural-deli.com/