Uwe, your info on this topic are very usefull. We are planning on doing the same in September. Our ship will be in Naples from 8:00 Am to 8:00 PM. We were thinking on doing the ferry or hydrafoil from Naples to Capri or Anacapri, then ferry to Sorrento and train back to Naples. We might skip Sorrento and go back to Naples to see the city. What do you suggest ? Also should we go to Capri or Anacapri ? Do you think we will have a chance to see the Blue Grotto ? Thank you very much for your answer.
Take the ferry / hydrofoil (h. is faster) from Naples Porto Beverello (next to the cruise center; left side) to Capri. The port there is on the north coast. Link to the map: http://www.premier.net/~Italy/capmap.htm
Another useful link: http://www.travelplan.it/capri_guide_getting_there.htm
From the Marina Grande you can catch a boat for the blue grotto. They start all the time. In front of the lagoon you have to change the bigger boat for a smaller one. Beware of seasickness. All in all you have to spend about two and a half or three hours for that tour. (Maybe in september there are not so many tourits as in june, july or august; so you could do this in two hours.) Than take the funicolar to upper Capri for a short walk. Go back to the port for Naples. I suggest to see a little bit of the ancient town of Naples. Sorrento? For me it ist not a must. Anacapri is in the middst of the isle oc Capri. Forget it, if you have not plenty of time.
Uwe, thank you so much for your fast reply. How do you suggest we come back to Naples ? By train or ferry (hydrofoil) ? If we take the train, do we get to see the view of the coast everyone is talking about ?
if you want to go to Sorrento, the train back to Naples is cheaper than the hydrofoil (and a little bit faster). But: you need about 15 minutes from the piazza Garibaldi (Main train station) to the port. I suggest to get back by ship. Riding by train you will not see much of the coast.