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There is good news and bad news. Bari is a total and utter waste of time perhaps the worst port of call I have ever visited. I honestly don't know why they call there. Here you either have to take a very expensive and long excursion beyond the port or my best advice is have a lazy day on board!! Its just a large, crowded industrial dirty city. Its also quite difficult to find your way around should you venture out on foot. Split on the other hand is lovely and you must get off and take a trip just down the coast either way. The seafood if you like it is wonderful. We actually hired a car for the day and drove and found a little restaurant is a quiet village just out of the city. The Bay of Naples and Sorrento is great if crowded but you have lots of opportunities there. Can't comment on the rest, but I have been told that Revenna is nice too.
Personally I never do ships excursions unless there are no other possibilities. If you do enough research - google is a wonderful thing if you type' cruise ports of call' you will find many sites offering suggestions on how to DIY. If you sign up to the site where fellow cruisers chat before hand you may find someone to share private tours with.
Have just returned from RCI Italy cruise and at Split passengers were tendered to the Port which is very central and Split is easy to walk round on your own. Ship's shuttle (5 euros return) from ship to centre of Livorno where you can buy a train ticket to Pisa or Florence but need to take a bus to the train station. Ship's shuttle to Dubrovnik (10 euros each way) takes you to the Pile gate where it is an easy walk round Dubrovnik or round the walls.
My advice on the two I have done of these is to do your own thing - Venice is easy peasy and with water taxi's buzzing arround and the water busses everywhere getting arround is fun -by the time you have taken a trip on a gondola ,visited St marks sqaure and the basilica remember long sleves or you wont get in be respectful they may not let you in with shorts on I cant remember but definately long sleves - loads of shopping, restaurants and if you have the dosh try Cipriano's taking their private launch from the sqaure across the canal -or the courts and the bridge of sighs and on and on , Magic place love it - -- Taorimina again easy to get arround friendly and filled with tourists.and remember to try the Broiche with ice cream world famous - great shops and restaurants and if you have more dosh sit out on the veranda having lunch in the Grand Hotel Timeo which is opposite the fabulous Roman/Greek Ampitheatre and looks out over the bay - or take an organised trip to Mount Etna all wonderful --