Tipical touristic places: San Telmo, La Boca and Abasto neighboorhoods to look for Tango culture and Inmigrants history. Also La Recoleta Cemetery. Palermo woods. Watching a football game. Eating an 'Asado' (Argentinean BBQ). Also pizza and ice cream.
If you understand spanish you could go to the theatre which is really good.
Nightlife is excellent! about 5 years ago
Tango and the street fairs are my favorite. San Telmo has the biggest fair which is on Sundays. The plaza Francia also has a good fair every weekend, which is right next to the Recoleta Cemetery. Shopping on ave. Santa Fe is fun. Night life is best in Palermo. There are also stadiums for futbol and polo. And take a tango lesson or see a tango show!!! almost 5 years ago