The financial crash of 2001 in Argentina resulted in a devaluation of the peso, which caused a significant foreign tourism boom. A result of this has been the emergence of a number of high quality Spanish schools that offer you the chance to study Spanish on a budget. In addition to cost though, there are further grounds for opting to learn to speak Spanish there.
(1) Few Argentines speak English. In contrast to countries in the northern hemisphere, which have greater contact with native English speaking tourists, businesses, and pop culture, Argentina has had relatively little contact with the English speaking world. Until recently, Argentines considered French to be of a higher standing than English and the people who had the means and interest to learn a second language tended to learn that language instead.
Even though attitudes are fast changing there now (English instruction now being an obligatory element of public school education), English is still seldom spoken fluently by Argentines. This represents an ideal situation for those wanting to learn Spanish as they will be forced to use the local language in order to get by.
(2) Argentines are easy to understand. Argentines do not talk too fast, nor do they mumble or swallow consonants, which can be common for Caribbean or Central American speakers. Many beginner students have difficulty differentiating between words with spoken Spanish due to them not being able to hear the stopping of one word and the beginning of the next and learning Spanish in Argentina reduces this issue.
You will of course acquire an Argentine accent when you speak Spanish, but this is no great problem, and you will still easily be able to be understood by Spanish speakers in other countries. In fact, having a slight variation on standard European Spanish can be a good thing, as when you speak in Spanish to natives of other Spanish speaking countries, they will be intrigued as to how you acquired your accent, making it a good ice breaker.
(3) Talking a lot is common in Argentina. You will find no problem in finding others to practice with because Argentina has a talkative culture and it is easy to start a conversation with perfect strangers. No one will think you strange or crazy if you walk up to them and ask them how they are doing and what their plans are for the day.
When Argentines find out that you have gone there specifically to study Spanish and to learn about their culture, they will be particularly welcoming, and you can expect to be asked to have dinner at their houses, and to be taken sightseeing. Confident learners will undoubtedly benefit from such an open environment.
If this sounds like an interesting opportunity to you, you just need to do a little research on the internet. Whether you prefer a relatively short month long study holiday, a half year home stay arrangement, or something between the two, you will be sure to find something in Argentina for you.