If you like landscapes you can take various shoots of Baia del Silenzio (Portobello). Try to walk on the way up to the Monastery and take some shoot at the end of the day. You will find also another way up to the Promontory, where you will find an old church destroyed during the 2nd World War. Go on until you reach the top of the promontory and you will find the Hotel "Dei Castelli" and the ancient gate of the Citadel.
If you like street photography you need to start from Baia del Silenzio and take the large pedestrian street from the cathedral of S. Maria of Nazareth to Place S. Antonio (just walk ultil you want!).