It's been a while since you posted, but we were on the Star Princess Greek Isles cruise in 2004, and have been on other Princess cruises that stopped by various Greek isles, so I'll try to respond and hope to hit some of the ports where you'll be.
Santorini: You anchor in the center of the old volcanic cone and tender in. The tender docks at the base of the mountain upon which the town is located; you can either take a tram up (I forget how much it costs), ride a donkey up (ditto for cost), or climb up the stairs--but be warned that you'll be climbing quite a height and distance on stairs on which many, many donkeys have left "reminders". After a wonderful day up top, you can take your choice of returns. We've ridden the donkeys up twice, stood in a line about three blocks long for the tram to return once, and walked down the steps the other time.
Athens: the ship docks at Pireaus, which is several miles from Athens. You can take a taxi into the city for about $40, or you can take about a 15 minute walk from the pier to the metro station and take the metro in; there's a stop at the base of the Acropolis, and you'll have a great day on your own. Just be sure to buy a metro ticket; sometimes Princess runs a shuttle bus from the dock to the metro station so be sure to ask. We've taken the metro to and from Pireaus twice and had great days in Athens.
Kusadasi: This is on the Turkish mainland, but the ship docks right in the heart of the city. From there you can share a taxi to the three main sights, which are Ephisis, the church of St. John the Baptist, and Mary's house--and spend as much time as you like at each place.
Rhodes: Princess provided a shuttle from where the ship docked into the old gated city. We started with a tour, but rode the shuttle back later in the day.
Mykonos: Princess provided a shuttle from the pier for the 15 minute ride into Hora, the main town. There are also two other buses, a private and the public bus, which have varying costs. We're walkers, so we just walked.
Katakolon: It was a bit of a walk into the city, but not bad, and it was along the waterfront. We shared a taxi to Olympia and spent the day. We agreed to pay him on the return trip, and the taxi driver was there to pick us up at the arranged place and time.
Corfu: We'll be there again in July. Last time there, we took the ship's shuttle into town.
Dubrovnik: It was quite a hike into the old city. There was also a bus, but we didn't have local currency for the driver. I'd say the walk was about 30 minutes, but it was very scenic and we enjoyed it.
Venice: The ship stops at a pier from which you can walk to Piazalle Roma, and from there you can walk across the Grand Canal to Santa Lucia railway station (to the left) or turn to the right and you can wind through the little streets to Piazza San Marco. It's a delightful walk.