It is difficult to give general advice about the most convenient university because that depends on your preferences, budget and the career you would like to study. Buenos Aires or the provinces. The most renowned universities are in Buenos Aires but for several careers there are excellent opportunities in the provinces. Buenos Aires has an excellent cultural life. In the provinces you will probably find a more quiet and relaxed rhythm of life.
Public schools are cheaper.
The most renowned is the University of Buenos Aires, which has excellent teachers in many subjects, and it is almost free. However as it is very democratic and open to all countries students it is probably overpopulated, especially during the first years of each career. Foreign students sometimes find it lack of organisation. In fact, they are excellent. Department of Foreign Students.