Leaving the ship early is as easy as packing your bags, checking out at the purser's desk, and walking off the ship -- but why?
Livorno is the gateway to Tuscany, including the cities of Florence and Pisa. Pisa, with its famous leaning tower, definitely is worth a visit if you have not been there, and Florence is famous for its art museums. The tour of the Tuscan winery (which includes a wine tasting) also sounds very interesting.
Also, the cruise line will have transportation into Rome already arranged for passengers who book hotels through the cruise line. If you talk to them nicely, you probably could hook into such a transfer at pretty nominal cost even if you arranged your own hotel. Also, Civitavecchia is much closer to Rome than Livorno so the transportation will cost a lot less even if you have to arrange it yourself.
Have a great cruise!