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Civitavecchia rail station is about a 15 walk from the dock gates (you won't get a taxi as they are only interested in taking you to Rome). The trains are cheap and run on time. See trenitalia website for timings and fares.
Livorno station is some considerable distance from the port. We found it quicker and economically justifiable to take a taxi from the ship into Pisa. From Pisa (after the tower) we caught a train to Florence. From Florence we got the train back to Livorno and then taxi to the ship. Timing is everything on this busy day and so check the trenitalia website for train times etc.
Naples appeared to be a chaotic place and we were glad we took an excursion there. Our guide to Pompei was excellent and well worth the extra.
Villefranche is easy. The train station is only a few hundred yards from the landing area. We went on our own to Monaco and it was very easy. It was just as easy to go the opposite direction to Nice etc. Try it. I wasn't brave enough to try the train in Civitavecchia but friends have assured me it is just as simple as in Villefranche. Hope this has been of help to you.
We went on this last year. Messina - we didn't do much here just went to the beach. Naples - we had a local taxi who took us to Pompei and then to Hercueneum. The cost was good and we really enjoyed doing both. If the weather is very hot Pompei can be unbearable. Civitavecchia - the train is really easy and well woth it. We were in Rome very early , did our sight seeing and were back on the ship by 3pm with no problems whatso ever. Livorno - there is nothing at Livorno you have to go to Pisa or Florenece. We took a bus to the train stattion then the train to Pisa. Didn't do Florence but by all accounts it is lovely. Villefrance is very easy to do whatever you want. A pretty place. Again Nice is easily accesible by train. The NCL is a lovely ship. We did all the resturants but the Tekanyanki?. I would advise booking up as soon as you get onboard as they get very busy. Enjo.
It is very easy to do these places on your own providing you do researc.