Have you looked at. Cruise Critic?
Catania, Sicily- go north to Mt. Etna and Taormina or south to Ortigia/Siracusa
Santorini- it will be very very crowded. Go to Oia. See Caldera views. Ancient Akrotiri. Cruise ship passengers will ride a gondola up and down the cliffs. Prepare to stand in long lines, hot.
Athens- arrange a guide to take you to Acropolis, Agora, Acropolis Museum, National Archeological Museum.
Mykonos-walk around Mykonos Town, wander the crooked alleyways, visit Little Venice, see the Windmills. If you have enough time, take a boat to Delos, rhe small island, archeological site, where Apollo and his twin Artemis were supposed to have been born.
Napflion- enjoy this charming waterfront town, castles. If time allows go outside of town to visit the ruins of the ancient Mycenae (Agamemnon) and the theater of Epidavros. One of the prettiest towns in Greece.
Katakolon- go to ancient Olympia! The torch for all Olympic games is still lit there. Goosebumps.
Naples- a large city with so much history, Archeological Museum, beat pizza in the world, go to Pompeii, Amalfi Coast, Capri. Many great choices.

I’ll assume your starting and ending in the port for Rome and that you are coming from the US or Canada. My first suggestion would be to arrive a day or two before your cruise starts. That way you have a buffer should there be any delays in your inbound flight and would allow time to adjust to time zone differences. Book a hotel at or near the airport. We stayed at the Golden Tulip about 30 minutes south of the airport. Rather than rush to Rome take some time to go to nearby Ostia Antica an interesting site similar to Pompeii. Extend your time in Europe and stay in Rome for a few days after your cruise. That way you can casually walk to see the main sites. In Valletta I would recommend going to St. John’s Co-Cathedral and the nearby Grand Masters Palace (Knights of Malta). Both are on Republic Street the main pedestrian mall in town. Of course a cruise down the main channel is also a good choice. You can easily get to Olympia from Katakolon. You can quickly get to Pompeii from Naples.