You can visit all of them independently. Villefranche you are tendered right in town - catch a bus/train to Nice/MonteCarlo. Livorno you can catch a train to Pisa or Lucca, Civitavecchia you catch a train to Rome. Naples you are docked right in town and right next to the ferry to Capri, and Palermo you are docked right in town. Do your research on Ports of call on a site called cruise critic. It is easy.
It all depends what you want to do at the various places. In vIllefrance you can spend an enjoyable day wandering there but if you want to go to Monte Carlo or Nice then walk eastwards along the sea front to the railway station and there are frequent trains, all along the Riviera. In Palermo you can walk into town and the back street markets and the cathedrals there are well worth visiting. In Naples you are also right in town from the berth but my advise is that if you want to go to Pompeii or Capri to go on an organised tour. Yes you can do them on your own but Naples is a chaotic city and a good tour guide brings Pompeii to life. I would say the same for Livorno as well and as far as Rome is concerned, yes you can easily get there by rail but if you want to get into St peter's the only practical way - without queing for 2 hours is to go on an organised tour which jumps the queue.