Buenos Aires is one of those cities where you can see the main tourist sights in 2-3 days. A lot of travellers hang around for a lot longer, but that is usually to take an extensive Spanish course or tango lessons, for which BsAs is the place to be. If you are not into those things, or simply do not have the time for it, and if you are not really a big city person (that would be the third reason to stay), then it is nice to get out of the city after some days.
That is pretty much what I did. On my arrival day I checked out the nice suburb of Recoleta and a bit of the city centre. On the morning of the second day I toke in most of the sights of the city centre. In the afternoon I met up with an ex-colleague and we had some coffee on the Plaza de la Mayo (his office is on the square, quite nice). Afterwards I walked a bit through the San Telmo area, and went to the suburb of Palermo in the evening, but most things were actually closed by then.
After waking up early again (that is the only disadvantage of sleeping right in the city centre with the window on the street side), I took the fast boat from Buenos Aires to Colonia del Sacramento on the third day. Colonia is an old, small, attractive little town in Uruguay, only one hour by fast boat from BsAs. I explored the museums and had a big late lunch at the quiet main square, before going back to busy, noisy, polluted BsAs.