Venice is small and easily walked IF you have a good map. The water taxis are easy and cheap to use.
Dubrovnik - walk the wall - 2 hours slow walking and picture taking - lots of up and down stairs - great views.
Corfu - Corfu town is interesting to walk, see both the Old and New Fortresses and the archaeological museum.
Katakolon - hire a local taxi to tour Olympia. Don't miss the museum at the site. Katakolon is a charming small village.
Athens - we walked to the train station, rode the train, and walked to the Acropolis. There are several other sites besides the Acropolis - one ticket allows entry to all.
Mykonos - a walking town. Three museums, all closed as it was too early in the season in April. It is pleasant to wander the winding streets and have a drink in a beachfront cafe.
Kusadasi - Hire a local taxi to Ephesus, which is very large. It was old before St. John came there and is very interesting.
Rhodes - we hired a local taxi and our driver, Dominic, was exceptional. He loved his island and it was apparent. Lindos has an archaeological site and is also a pleasant town to explore. In Rhodes Town the Fortress of the Knights is interesting but be aware the Palace closes at 3:00 p.m.
Santorini - ride the donkeys or cable car to town. Akrotiri (Minoan archaeological site) and the museum are both closed Monday, which is the day we were there and that was disappointing. But the town is charming in the style of Mykonos.
Naples - hire a local taxi to Pompeii and/or Herculaneum. Naples also has a large and interesting museum. Traffic in Naples is fierce!
Rome - use the local city buses. The bus routes are clearly marked and 4 Euros will buy an all-day bus pass.
In all these places, try to obtain a GOOD map. The maps in the Princess port literature are grossly inadequate.