We've been to the Greek isles twice, once on Disney (out of Civitavecchia) and once on Virgin (out of Piraeus). First, I MUCH prefer the cruises out of Piraeus because as mentioned before, Athens is one of those places that is better to have a day or two to roam rather than a stop to do a single excursion. We did the latter on the
DCL cruise, but since the Virgin cruise went out of Piraeus, we had more time to properly explore Athens, just rambling through the Plaka and surrounding areas and it was fantastic. I didn't get a good picture of Athens from the first visit because the traffic was insane. If you fly in/out of Athens, you can avoid most of that by just using the Metro. The dining in Athens is fantastic. If you can, make some time to have a meal.
For Santorini (if you go there), we have found that doing an excursion is a must, simply because you go to the ferry port and bus up the hill (BTW, you will need to close your eyes for about 5 minutes on that drive!), so you avoid the chaos that is the cable car. That said, we found the cable car not to be so bad heading back down, so there is that. (Quick note: one great thing about our Virgin cruise was they announced the morning that we got there that they had cable car passes, which are 10 euro each way, free for everyone and if you were doing an excursion, your guide would hand them out to you if you weren't returning to the ferry port). Also, make sure to try to get to Oia as soon as possible in the morning, It gets insanely crowded there.
Mykonos is my favorite Greek Island. You really don't need an excursion here. For our DCL cruise, we were at the dock (about a mile or so from Mykonos Town) and DCL provided a free bus to and from the town. On Virgin, we tendered, but it was about a 3 minute tender directly into town. If you haven't been here, just lose yourself wandering around town. It's magical. Also, Virgin overnighted and spent two days there, so we got to do the town and a beach the next day in addition to experiencing Mykonos Town at night, which was even better than daytime there!
We also visited Corfu on Virgin. Not sure how DCL will handle it, but Virgin provided free bus transport from the Cruise Terminal (which you take a bus to from the ship) into the heart of town. Again here you can just wander around if you want. Corfu town has its own charms. Quick tip. The Starbucks here has the entire Greek Coffee Mug collection available for purchase (if that is your thing... there's one in Mykonos as well, but it's a hike). The old fort is worth a hike as well just for the amazing views up there. Lastly, get a souvlaki or greek salad at Pitta Pappou... you are welcome...