Florence shore excursion question

The RCL western med cruises that stop in the livorno port at 8:30 am until 8 pm we were thinking of booking a private drive or tour from the cruise line to take us to the florence city center we mainly want to see ponte vecchio walk inside the duomo walk around a little then head to san gimignano and back to the ship . Does anyone know if we would have enough time to do this if the cruises is in port from 8:30 am until 8 pm?

Yes, you should have plenty of time to do as you suggest. I would contact the tour companies you are considering and ask them the best routing. If you left the ship as early as possible, you'd probably have enought time to add in Siena, which is a wonderful stop, amazing cathedral, etc.

As lovely as San Gimignano is, there's not a lot to do there other than shopping and eating, although you can climb one of the tallest towers which is fun. So an hour there is probably plenty. . .