My favorite thing we did in Buenos Aires was probably go to the Catedral de Tango where real Argentineans go to dance. It was no touristy tango spectacle, just a big, dimly lit, warehouse-like space with table on one side a dance floor on the other. There were different sorts of modern "art" on the walls and a big picture of Carlos Gardel, one of the most famous tango dancers ever (who by the way both Argentina and Uruguay claim as their own).
We got there at about 11:30 PM and the locals didn't start arriving until more like 1:30-2 AM. The dinner off the menu of the day was delicious--some sort of baked squash with cheese. I enjoyed sitting there listening to the beautiful tango music and occasionally sneaking peaks at the couples on the dance floor. We didn't end up leaving the catedral until about 4 in the morning, and apparently that was an early evening for most South Americans.