I enjoy cruising but don't take organized shore excursions. They are expensive and generally not my speed.
I might make an exception for a must see that isn't possible without the tour. Since that hasn't happened yet, I'm still waiting to take an excursion.
Instead I research ahead to find out transportation an activity options. A fun way to go is to stick with some friends from the ship. I've pitched in for a twelve passenger van and driver who took us where we wanted to go for a fraction of the excursion price and much less than a taxi. I've had great experiences when drivers take us to places they like that aren't on anyone's tourist map.
For Rome, you can take a train into town faster than a bus that has to drive in traffic. Unfortunately, you won't have time to see much of Rome. Many of your stops have concentrated touring, so a taxi into the center for a day will be just right.