We did the opposite this past June. We sailed the Millie from Barcelona to Venice. Celebrity is outstanding at cuisine, ambience and service. However we thought entertainment was lacking. Depending on your age, that might not matter. But we like to stay up after 10:00 and there really isn't a lot to offer passengers. However you'll be in the Med, which means long days and early mornings, if you want to see as much as you can.
At the port of Livorno you have to decide if you want to see Pisa or devote all your time to Florence. Trust me when I say you can never have enough time in Florence!!! Pisa is really just the tower. Not really worth the 2 or 3 hours out of your day.
The same dilemna faces you in Villfrance. Nice or Monaco? Doing both is a long day. We have been there 3 times and last time we journeyed to Cannes for a great day by the sea.
You will certainly enjoy your self.