I am sure that you can do your own thing from there but I suggest that you google " Marina di Carrara" (please spell it correctly) and do your research that way . .... Neil.
I did send a reply earlier but because I mentioned a certain word it appears to have been withheld So..... Look up Marina di Carrara, you spelt it wrong by the way, on the web and it will tell you loads about the port and like most places in the Med you can do your own trips easily with public transport or mor expensively with taxis. A hire car is an option but only if you are a very competent driver should you tackle Italy. .... Neil.
Here is the Thomson web page on this port of call: http://www.thomsonbeach.co.uk/th/cruise/viewPortDetails.do?portCode=005186.
The was not a lot in Marina di Carrara itself but the port had abus service up the mountain to Carrara which has shopping facilities. Carrara is famous for it's marble which was used for the statue of david and you can visit the quarries further up the mountain. Pisa and Florence are also within commutable distances on the train. When our ship stopped at this port in Oct quite a few people who did their own thing and visited both Pisa and Florence but only managed an hour at each location due to having needed to be back at the ship .
We were at this port in August unexpectedly instead of Livorno. Public transport was a little thin on the ground as it was a Sunday. It was also too far in a Taxi. But we tried the local beach about 15 minutes walk and we had a great morning there. The mountains in the backgrond are a great sight. Enjoy!