Amalfi Coast, Italy
Sorrento is accessible by train from Naples or Rome. The Circumvesuviana train runs from Naples to Sorrento every half hour or so and takes just over an hour. It has a stop at Pompei so you could stop on your way to see the ruins. There is also a train called the Campania Express which can take you to the Amalfi Coast. Be careful of pickpockets on the train. Driving and parking is difficult on the Amalfi Coast. I don’t recommend renting a car.
Buses run regularly between Sorrento, Postitano, and Amalfi. There is also a route from Amalfi to Salerno. Tickets must be purchased at a tabaccherie, bar or café.
There’s ferries operating between several of the towns along the Amalfi Coast including one from Sorrento to Capri, but they won’t take you to the Blue Grotto on Capri. Not only will they get you to your destination, but the ride is a visual treat.