I always have "advice" but not sure anyone ever listens (or should listen). Rome is a very large sprawling city. It is probably the only city in Europe that I recommend first time visitors take a tour. Ideally, it should be an all day tour whether by the cruise line or a private company. I particularly like the tours that take you through the Vatican and use various schemes to avoid the long lines (and thus save a valuable hour of the day). And of course you should see the Palentine Hill area, Collosseum, the Spanish Steps and Trevi Fountain. That being said, it is very easy to get to Rome on your own via the train. So, if you have some travel smarts, do your pre-trip homework, and have the spirit of adventure, you can save a lot of money by taking the train to Rome.
Livorno is different. I think Florence is where first-time visitors should spend their day, and Florence can easily be done on your own with a simple guide book/map. Whether you use the transportation provided by the cruise line (usually about $65 - $80 pp) or take the train (about $20 pp) is a matter of choice. The biggest hassle is getting a taxi to take you from ship to train station, but a little persistence with the taxi drivers will usually get you a driver. In Florence, everything is pretty much within walking distance except for the Academia. Many go to Academia just to see David (we have done it) but the truth is that it takes some time to get out to that museum, you have to normally wait in line (it is possible to buy tickets in advance on-line), and all this to see a great statute that happens to have a darn good copy sitting in the piazza Della Signoria. Many also like to spend half their day at the famous Ufizzi Gallery, and my only comment about this is that if you were making your first visit to New York City, and only had one day, would you spend it in the Metropolitan Museum of Art? Personally, we find the renaissance art of the Ufizzi to be dark, dreary, and somewhat boring (I will get flamed for this comment). However, we do think the Ufizzi building is a beautiful structure. On the other hand, when we are in Paris we skip the Louvre in favor of the Musee d'Orsay. Its a matter of taste, but the impessionists make me smile, and the dreary dark renaissance art makes me feel dreary and dark. Imprssionism got its start because even the artists were bored with the old style.
Ok.. I have had my fun.