What a wonderful itinerary! We visited about half of these ports on our Western Med cruise (on another cruise line) in 2010 -- started in Barcelona, then Monte Carlo (shore excursion to Nice), Florence, Rome, Naples.
What activities interest you most? History, architecture, beaches, general sightseeing? We are history buffs who like to fit in as much as possible on a first visit, so we did all-day sightseeing tours in Monte Carlo/Nice, Florence and Rome, and visited Sorrento and Pompeii from Naples. Two important items to note about these tours. First, there is often a lot of walking involved as many streets are too narrow for tour buses. So, wear comfortable shoes AND bring a lot of water. Second, Florence and Rome are not close to the cruise terminal, so you'll either have to rely on cruise line transportation or public transportation. We did cruise line excursions in all of these ports, but that is personal preference.
Let us know what interests you? Also, will you have kids with you?