There are many choices for learning Spanish in Buenos Aires. It is not the Spanish that is spoken in Mexico, the key differences being the use of vos, no vosotros, and the pronunciation of ll and in some cases y is like "ch" instead of "y". Given that there is a lot more to learning Spanish, even if you want to end up needing to speak Mexican Spanish, there is no harm is learning the Spanish as spoken in the Río de la Plata region. Especially given the numerous other attractions in Buenos Aires, it is a great way to spend time vacationing and learning Spanish if you have a month or two or more to spare. Just be prepared to hear the sound "ch" a lot, and hear rapid delivery of words, speakers here tend to roll on from one word to another without pausing!
Instituto de Enseñanza Superior en Lenguas Vivas "Juan R. Fernández"
A web search for Spanish in Buenos Aires will result in many hits, but no results page includes the school that locals hold in high regard. [Such is the world of automated search, poorly linked web sites are considered of low importance!] Locals speak highly of IES Lenguas Vivas "J. R Fernández", which is at at Av. Carlos Pellegrini 1515 (corner Arroyo), in the Retiro section of Buenos Aires. The phone number is +54-11-4322-3992. They teach many languages here, including Español para Extranjeros. They have a rudimentary web site that does not work on Firefox but works on Internet Explorer - non-working IES Home Page, and anyway it does not contain information on the Spanish programs.
Of course, I did not know about their reputation at first, I just stumbled on this school since I spent a lot of time walking around in Microcentro and Retiro. That was when I saw a odd looking entrance between tall building, with a board stating it was a school for Idiomas. This was the IES en Lenguas Vivas "J. R Fernández" at Av. Carlos Pellegrini 1515. It is a Government of Buenos Aires undertaking, so the service is like slow government offices anywhere, and information is hard and impossible to get. This felt like a good challenge, and after standing in a long line, returning twice to find the people I was supposed to get information from, I finally got the details on the courses they offer.
In 2007, they used to have a 1 month intensive course, for around AR$340 for 48 hours of instruction, which was an amazing deal since most other similar classes here would have cost AR$1200 or more. This course is no longer being offered in 2008.
In 2008, I repeated the same agonizing process to get information (which is painful if here for a short while only - it is impossible get any information over the phone unless one already speaks Spanish, and most of the time no one picks up the phone. And forget about sending email to any of the email addresses you may find for the Español para Extranjeros program - there will be no reply).
In 2008, the intensive course was now a 2-month affair, running only 6 hours/week. And the fees were on a "pay as you can" basis - great deal for students, backpackers on a tight budget with no money! [If you can pay, use the old rate as a guide, around AR$7 for every hour of class or two, or a fraction or multiple thereof, as your pocket permits!] The text book used for the Basico2 level in 2008 is quite expensive though, at AR$79, back in 2007 the information I received was that all course material would be included in the cost. Signing up will require a copy of your passport page, keep one or two copies on hand always when in Argentina, since purchases for mobile phone SIM cards, boat to Uruguay also require passport information.
Given that the information and registering for these classes was so hard, I thought there would be few to no additional other students - but the classes were packed. They have a Basico 1, Basico 2 (which I attended for a few days, had to cut it short), Intermediate, etc. Talking with other people who were in the lines when I tried to get information I discovered that these classes are quite well known by the locals, and the teachers and this school have a very good reputation. Locals recommending a Spanish school - that is a very good sign, so all the trouble of registering is worth it. I attended the Basico2 course for a few hours and then had to cut it short because of vacation timing problems but the teachers were great, the rest of the students in the class of around 10 students were a great bunch, so it was a very good experience. It is a good environment to listen and speak in Spanish-only, and have the discussions go on in various directions that were quite useful to the first-time Spanish learner.
The process for registration is a complicated as mentioned above, and the courses usually start around the beginning of every second month, with nothing in summer (Jan/Feb). For all courses other than Basico1 there is a evaluation test, which usually takes place 1-2 weeks before start of the course. If you are getting information, and you see a long line (> 10 people, can be 100s during registration days!), just give up - come some other day! The Oficina de Cursos is a very slow office, so even 5 people in line means 30-50 minutes of waiting! If there is a long line on the first day of your course, browse around on all the walls around that office - there will most likely be a sheet with information on the class-room where you need to go for your class, this information is not available at the information desk.
With 10 hours of this class under my belt - I could not stay for the entire two months, even with the addition of numerous hours of listening to Spanish lesson , audio CDs, buying numerous text-books, my Spanish continues to be poor - ¡estudio mucho, pero no aprendo mucho!
Centro Universitario de Idiomas
Having done extensive research on learning spanish in Buenos Aires, I had another class in mind if IES Lenguas turned out to be a non-starter. Centro Universitario de Idiomas, at Junín 222, with a web site that claims some connection to the teachers at Universidad de Buenos Aires, and an email reply I received had the signature with this address: International Studies Department, University Language Center, School of Agronomy, University of Buenos Aires. They respond to email promptly, and the web page has extensive information, so getting information and signing up is a breeze for this course. Their ads also are all over billboards in the city, for English and other languages. They do have intensive 4 week courses in Spanish. Centro Universitario de Idiomas-Español is their web-site, and the cost for 1 month course in 2008 was US$400. Phone: +54-11-5238-3044.
Universidad de Buenos Aires
Regular courses for 17 weeks, intensive courses for 8 weeks, and special 1 month courses in Jan, Feb and July. All information on the web site: Cursos de Español en el Laboratorio de Idiomas. Cost is nearly same for all, around AR$1100 in March 2008. They are located at 25 de Mayo 221, phone number is +54-11-4343-5981.