Visit the Cemetery at Ricoleta
Go to the markets in San Telmo
Take Tango Lessons
Grab the Lonely Planet Guidebook for some more ideas.
My stay in a hostel sorted a lot of these things out, either with guided tours or other travellers simply walking to the local sites & activities. about 10 years ago
How old are you? Its hard to say like these. Tango show, bomba del tiempo, empanadas at junin y peron (those are the streets its the best empanada place for the majority of portenos i know from the central areas...really good those last months it has been always full of tourists), go to a boliche if you are young (mandarin or liv...jet its fun as well. The most famous is asia de cuba but its not great). Happy hour bar for all ages (18 to 40): gibraltar. Take a look at the malba website to see whats up there when you are here, cultural life here is big. about 8 years ago
I would consider 2 weeks in Bs As a waste. In that time period I would try and get up to Iguazu in Missiones, Mar del Plata, Rosario etc. There are so many exciting and beautiful places in Argentina Bs As is such a small part of the country and so different to the rest of the country almost 8 years ago