Yeah, actually there are many good veggie options in BA. In addition to vegetarian restaurants, there are also usually good vegetarian options at restaurants that do serve meat, even in this steak-and-ham obsessed country. Here are a few of my favorites:
Prana - 5105 El Salvador, Palermo - breakfast, lunch, and merienda - small and chill
Bio - Humbolt 2199, Villa Crespo - nice veggie stuff
La Posada Natural - Sarmiento 800ish, Microcentro - cafeteria style, lots of yummy integral stuff
Pura Vida - Uriburu and Rodriguez Pena, Recoleta - juice bar with vegan food, big delicious salads and awesome mediterranean wrap
Tea Connection - one on Uriburu in Recoleta and one in Puerto Madero - not vegetarian but lots of veggie sandwiches and offerings
Mark's Deli - El Salvador and Armenia, Palermo - same as above
Vegan is harder to come by than vegetarian, but for veggies as a last resort this is a country obsessed with pizza . . . just make sure they dont put ham on it (they love that here). Also if you want to eat in, not at a restaurant, there are dieteticas all over the city which are little grocery stores selling lots of whole grain stuff and they usually have refrigerators with milanesas de soja, good veggie tartas and empanadas and stuff - check it out. I hope that helps!