I have merged your post with one already open on the Island Escape. You should find some useful information in earlier posts.
There is some information on doing ports DIY HERE, but I don't think the ports you have listed are mentioned. You can read reviews of the ship by clicking on Cruise Reviews at the top of the page.
We are doing the same itinerary on the Island Star on 19 August so I'd be delighted if you would post a review on your return.
We did Florence and Pisa on our own on two separate trips. You catch the bus or a taxi to the train station in Livorno and get the train from there. We shared a taxi from the train station in Pisa to the Leaning Tower with another couple from the ship who we met on the train.
You can find the train times HERE
We took an organised excursion to Pompeii last time we were in Naples and I can highly recommend it. This time we're not sure whether we'll take the hydrofoil to Capri or to Sorrento.
Apparently you can take a train then a bus from Messina to Taormina, but I don't have the full details.
HTH
Have a great cruise and remember to come back and tell us all about it!
luci
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