To get everywhere in Italy, you can always take the trains from Napoli Centrale:
Check the website of these two companies for train schedule and discounts. Italo offers high-speed trains and Bus (They do have a stop at Sorrento). Trenitalia offers both high speed trains and regional trains.
DISCOUNTS
FINES CAN BE AS HIGH AS 500 EUROS AND UNPAID FINES CAN GET YOU STUCK IN ITALY OR GET YOU RED FLAGGED FOR THE NEXT TIME YOU COME BACK TO ITALY.
With the train and bus network, EVERYWHERE is reachable!
Some popular destinations for you: Napoli, Roma, Firenze, Venezia, Salerno, Bologna, Verona,...
Some secret places: Matera, Caserta, Bergamo, Cremona