We love helping independent travelers but Livorno does have its challenges. Much depends on two factors: how fast you can actually get off the ship and how lucky you are in getting a taxi to take you to the train station (many taxis do not want to do this short haul). By the way, you can expect to pay about 20 Euros for a taxi to the Livorno train station and if you would have another couple it gets that cost per person down to 5 Euros. At any rate, if you look at the train schedule (and they are usually on time for this route) there is a 7:30, 7:43 and 8:11 (if you miss this it would be 9:11. My advice is to work with the assumption you will make the 8:11 (get off the ship fast) although we have personally made the 7:30 at times. This means you will be in Florence at about 9:30. It would take you nearly a half hour if you wanted to walk to the Academia, but about 10 min if you grab a taxi. If it were me we would try to get a reservation for about 10:30 which gives you time to relax, perhaps have an expresso, and walk if you like to take long walks. Do the Academia first thing since it will be your furthest point from the train station. You can then get back towards the center where you have lots to see, plenty of nice cafes for lunch, and an easy walk back to the train station. Do not cut it too tight on your return to Livorno since there is often a shortage of taxis waiting at the train station. You should be back at your ship by 6:30 which for us, means you should plan to be back in Livorno by around 5 (to play it real safe). The return trains all leave at 27 min past the hour and take about 1:30 so we personally like to get the 3:27. There are plenty of others that will cut it closer and take the 4:27 but this is a bit risky if the train is late and if there are no taxis.