From Airport to Central Train station: Alibus airport transfer bus from outside the airport terminal (4 Euros towards Napoli Garibaldi Centrale Stazione (Train station) and Napoli Porto (Port of Naples).
For more information: http://www.napoliunplugged.com/naples-alibus-airport-shuttle
From Airport/Central Train station to the Department of Political Science: Information on how to get to the Department of Political Sciences from the airport and the main railway station: http://www.scienzepolitiche.unina.it/?page_id=41
Some things to see:
Centro storicoVia dei Tribunali (Pizzerias)
The Amalfi Coast