Hi Alyona,
In addition to tango I would recommend going to a few Jineteadas (Argentine rodeo) to get a real feel for Gaucho life. These are very non commercial, country events where all the genuine gauchos dress up in their traditional gear, listen to bands, eat asado (you buy suckling pig at 30 pesos a kilo - bring your own knife), watch the rodeo and talk about horses (the argentine passion). The people are incredibly friendly and the horses amazingly wild. It is hard to take a bad photo at these events - I know because while my girlfriend is a photographer by trade, I am a rank amateur and even some of mine were brilliant. There is so much natural character on show that the skill is really just being non intrusive and getting to chat to them.
We would be delighted to take you to one, or some decent polo games if that interests you.
Miles