You mean La Plata and not Mar de Plata, right?
Just clarifying.
La Plata is an hour away from Buenos Aires and a taxi may be your best bet.
There is a taxi stand just outside customs or you can try a transportation company called Manuel Tienda Leon.
If you are going to Mar de Plata - that is 5 hours away by bus and you can take a bus at the bus station in Buenos Aires - Retiro.