Located on a nondescript little corner in San Telmo is El Baqueano, a restaurant dedicated to carnes autoctonas (native meats). I've been visiting the restaurant for several years now and have probably been 6+ times.
It is a multi-course tasting menu which evolves from time to time, and after not having visited for about a year, the most recent visit had the largest menu evolution between visits. From alligator to llama to river fishes and so on, the preparations would have people lined up the door in NYC or SF. While I don't always love every bite, it has been my favorite restaurant in the city for some time. Genuine and lovely service, a well-curated wine list, it is always an interesting experience. It is also such a different experience than most eats in Argentina.
It hit #15 on this year's "Best 50" in Latin America list. http://www.theworlds50best.com/latinamerica/en/The-List/11-20/El-Baqueano.html