Buenos Aires: great city, great party, lots to do.
Mendoza: another beautiful and interesting city, very close to the Andes, mostly sunny and LOTS of wine.
Bariloche: the Patagonian jewel, the Bavaria of the south, amazing in spring, snowy in winter. Sky, rock climbing, hiking and eating chocolate are some common activities there.
Misiones-Iguazu falls: amazing, wildlife, ionised water and a fantastic view…. Usually packed with people, but worths a visit.