Livorno : A shuttle bus will be provided from the port to the centre of town. It is a few miles away & not worth walking from the port (even if they do allow you). Using the train is perfectly possible from here, if you are ready to grab the first shuttle bus, have your Euro's ready for the bus ticket & happy to explore. To get to the station walk back to the busy square near the drop off point, & you will see various bus shelters, in these shelters you will find the ticket machines - buy your tickets from these machines, should be 1 Euro (buy one for your return journey too, and keep it for later - DON'T frank it now). You can buy tickets on the bus, but they are a LOT more expensive. I'm pretty certain that it is still bus #1, but the locals are very helpful, so check with them. When you board the bus, you MUST put the ticked into the franking machine for a date/time stamp. Each ticket lasts 1 hour from the time you frank it.
You can get a bus to Pisa, but it stops everywhere & takes a couple of hours. The train is only a short run. The tours office will sell a Florence & Pisa day trip, but it really is a lot to take in one day, but if you are travelling all the way over for this voyage, you may feel it is worth the effort, just make sure you are ready for it. If you are "all toured out" by this time, Livorno is an interesting town to wander around, but you will probably be back on the ship within a couple of hours, so we would definitely reccomend Pisa, Lucca, or Florence.
Naples docks close to the city centre, exaclty where depends on which other ships and cargo carriers are in port on the day. But if you look ak maps.google.com & search for Naples, Italy, then switch to Satellite mode & zoom in, you will see a few ferries & ships in the port.
Venice : please check that the ship is going to moor up there, as some go to a town called Trieste which is 80 miles away & with no easy public transport link. Hopefully you will be moored up 'out the back' of Venice near the railway station. You can either walk the main sites, or buy a Vaporetto (water bus) pass which allows you to hop on & off the buses & see all of the area, from St. Marks, to the Lido, to Murano & Burano. The Vaporetto website is http://www.actv.it/english/navigazio...iffe_vaporetto
and has all the routes, timetables, and TouristCard special prices.
Hope that helps,