Welcome to Cruise Chat Mike!
Well the easy question to answer in your post is which Station in Rome is best- Rome Termini. There are also many good hotels within a couple o city blocks of the station. I can't be certain for the train station in Naples. There is a train station that we used to go to Pompeii and it did look like it was a big station, but I was not trying to travel to Rome from it so I never looked. IF that is the correct station (See our "Train Travel in Italy" post at the topic of this section of cruise chat" then is is only about 1/2 mile from the port (probably would be best to grab a taxi if you have a lot of luggage.)
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013