Doing Livorno (Florence) is very doable on your own. Get off the ship as early as possible and take a cab to the train station (Livorno Centrale). Train to Firenze SMN is about 1 1/2 hours.
Check the train shedules at Italian trains
to get a grouping of times for going to and coming back. Give yourself some leeway on the way back. All the trains are 'locals' and prone to delays.