tommycruiser,
Welcome to Cruise Crazies.
While in Barcelona, if you have time, visit the Gaudi Cathedral (La Sagrada Familia), which is an architectual wonder in Barcelona designed by Gaudi himself. Also if you have time take a trip to Montserrat. There you will find a monastery and cathedral dramatically perching on the top of Montserrat. There are also shops and a hotel high in the mountains. There are some scenic views of the valley from atop Montserrat.
When you're in the Villefranche-sur-Mer area you have to work your way up to Monaco-Monte Carlo. The ship may have an excursion to Monte Carlo. When you get there make sure you get your passport stamped at the Monaco-Monte Carlo train station so you can have bragging rights. See the palace and the route for the Grand Prix Auto Race.
From Livorno you can take a trip to Pisa (Leaning Tower) or Florence. Shopping is great in Florence. Look for Italian leather. There's also the Duomo Cathedral that's seen from all around Florence and the Ponte Vecchio bridge that spans the Arno River that has shops on it too.
There's not much to do in Civitavecchia. You'll have to take an excursion to Rome. You may want to take an excursion to the Colleseum, the Vatican, the Spanish steps and some of the famous fountains in Rome, like Trevi Fountain.
In Naples you might want to go to the ruins of Pompeii or the Isle of Capri, both very exciting.