Check out the disabled cruisers website at ***Edited for commercial content*** esp. the archieved information about Europe.
In Barcelona we found wheelchair accessible cabs (left over from when the Paralympics where there). Our cruise line (Princess) was able to arrange these for us (we had to pay though). They may not have English speaking drivers though, so know exactly where you want to go. The Rambles is fairly accessible and you can walk around the old Gothic area from there (not all buildings are accessible though). I believe the Christopher Columbus museum and the Picasso museum are accessible. You can find some information on Spain here:
Since the Paralympics are in Athens later this month, I would expect to find much better access there by the time you arrive. In fact, the Parthenon is NOW accessible with a temporary elevator that is being replaced with a more permanant structure. You may be able to find more about tranporation as the Paralympics evolve....perhaps contact some returning athletes??
In Italy there are some private companies but they are VERY expensive.
If you can transfer to a car, then you may consider taking a cab in Livorno to the train station, which is accessible, and taking the train to Florence. You will need to plan your time carefully to be sure you don't miss the ship coming home. You can get around much of Florence with a manual chair, and some of the museums have elevators or lifts.
Venice is not very accessible as most of the bridges have many steps, so be prepared to both tender here and to need to get help lifting a manual wheelchair if you want to see anything beyond San Marco square. I understand that some of the vaporettos are accessible so a boat ride around the canals may be the best bet. Here is an article to review:
In Naples you dock right downtown and can push around the shops downtown (see the Galleria at least) and over to the old fort, which is partilly accessible. We did go to Pompeii....it was quite an expedition. We lifted my mother into a regular bus, then bumped up a few steps and a very long and steep ramp in Pompeii. The cobbles, etc. were VERY difficult even with a manual chair, and we made the mistake of not going out the entrance, but down the 6 flights of stairs to the marked exit only to find a non-accessible turnstyle. Never want to do that again, but my mother got her wish to see Pompeii! Many people in Naples had a good time on the drive on the Amalfi coast, which might be a better option.
Check these out: