We took a marvelous tour out of Naples. NCL called it Flavors of Sorrento & Pompeii. It took us south to the Sorrentine Peninsula (to visit the coastal village of Sorrento and a family-owned farm in the hills above the village), the ruins of Pompeii, and a cameo factory. It was a long day, yet well worth it. Pompeii is a must.
You can also do this on your own (see the Europe section, as Dave suggested).
We did a walking tour in Rome, again through the cruise line. But, you can do this on your own, too.
The most important suggestion I have for a Med cruise is to bring very comfortable walking shoes.
We exchanged dollars for euros before leaving home. We also used ATMs in port, if needed. (Let your bank know in advance as they will have advice on using your PIN overseas.) Get some small bills for tips.