Do you have room in your suitcase for me? I do laundry, prepare snacks...just kidding! Have a fabulous time!
Make sure you throw a coin into the Trevi Fountain (remember the movie, "Three Coins in the Fountain"?) - to do so guarantees that you will return again to Rome. Visit the Pitti (spelling?) Palace - great artworks, The Forum, The Vatican (of course) and basically, just walk around if you can. Stop for espresso and gelato (ice cream). Look for small restaurants where the Romans eat.
Your cruise director can point you to onshore tours, but I agree, if you can, hire a private car and guide.
Rome is a great city to visit. I haven't been there in 40+ years, but someday I will go back. After all, I did throw a coin into the Trevi Fountain!
Anita