Lourdes. Whether you consider the reproduction cathedral and grotto an act of faith or a Disneyland throwback, it's still worth a visit. Urquiza line train from Lacroze station in Chacarita to Lourdes station or San Martin line from Retiro to Santos Lugares. You don't really need directions from either - just walk towards the twin spires - but the nearest main intersection is La Plata / Rodriguez Peña if you want to find it on a map. Enjoy.
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).