One hour by car to the west, Lujan has a lot of stuff to pack in one day. The National Basilica (its street level and underground) , the Museum of Transport, the Museum of Colonial History (the biggest of the country), the religious stores, the little river with games and attractions from the 1950s and 1960s, it is all there. Plus no foreign tourists. And it is also a nice middle sized town with a central square and stores.
Take the bus 57 from Plaza Italia in Palermo to LUJAN, or go by car (Autopista del Oeste, turn only when you see the exit for the BASILICA, don't worry, the thing is very visible).
I forgot to add: go early and on SUNDAYS.