If you are short on time and want to take a lot in, Naples Sightseeing Buses are a good alternative. Here a few good options:

Naples Hop On – Hop Off City Sightseeing Buses

Pompeii-Vesuvius operated by EAVBUS

SITA Bus to/from Sorrento, Positano and the Amalfi Coast

Sorrento – Rome

Campania ArteCard

If you buy a 3 day, Tutta la regione (the whole region) Campania ArteCard, for €32.00, then all your transport (using road transport (buses, trolleybuses); and rail and cable transport (Metro Line, funiculars, trams, Circumflegrea, Cumana and Circumvesuviana trains) within the region is covered for those 3 days.  If you buy a 3 day ArteCard Napoli, for €21.oo, then all your transport (using road transport (buses, trolleybuses); and rail and cable transport (Metro Line 1 _ Metro dell’Arte, Line 2, Line 6, funiculars, trams, Circumflegrea, Cumana and Circumvesuviana trains) within the urban area of Naples is included.