For the other ports, you are looking at bus or train trips of 60-plus minutes to reach the major tourist spots. Each port will have a free shuttle taking passengers to the port's gate. From there, you would need to make your own travel arrangements.
Train service is the fastest and most affordable option. Economy tickets from Livorno to Florence start at $19 each way and Naples to Pompeii start at $8 each way. Details: www.raileurope.com. Circumvesuviana offers train service from Naples to Sorrento for about $5 each way. Details: www.vesuviana.it/web/en.
Keep in mind that some cities have more than one train station. Also train strikes happen often in Europe, which may require last-minute change of plans.
Most cruise passengers who want to see both Sorrento and Pompeii opt for some type of tour. You can find guides with private drivers for your group of four starting around $180. Two that come recommended are Italy Cruise Tours (www.italycruisetours.com; 201-204-9020) and Italia Tours (www.italiatours.com; 800-283-7262).
One final note: If you go it alone, be sure to give yourselves ample time to travel back to your cruise port. Only excursions arranged through the ship guarantee to wait for passengers who may arrive after all-aboard.
Last week we recommended some Paris Museums to see while the Musee d'Orsay is being renovated. One astute reader noted that travelers should take advantage of the Paris Museum Pass, which offers discounted admission and allows visitors to bypass ticket lines. Details: http://en.parismuseumpass.com.