Greek Isle Cruise

Since it is both your first cruise, and visit to Greece, I'd recommend that you get Ricks Guidebook for Mediterranean Cruises. It's got tips for both cruising and handling port stops, as well as the usual info on the major sites to see.

For cruise advice, have a look at the Cruise Critic website. It is a huge site, but has separate forums for each of the larger cruise lines, plus forums on ports of call.

Athens- visit the small, special Cycladic Museum and go up to the top of Lycabettus Hill for sweeping views of Athens all the way out to the sea.
Acropolis Museum and National Archeological Museum are both excellent to visit.
I know Rhodes has been having fires but if possible spend time in Rhodes Town and have lunch at Hatzikelis, a wonderful Greek taverna. We have eaten there several times.

Go to the cruise critic boards. The advice on Santorini and Mykonos is more thorough than what you will find on this site.

In Athens many people miss out on the Agora. Very historic, usually not crowded, and one of the best preserved temples in the country. In Mykonos you should take a short ferry ride to Delos which is often referred to as the birthplace of the gods. Google them and see if they appeal to you. Oh, in Mykonos, if you stumble upon a place called the Rhapsody Bar, do pop in. Very quiet, cool, and great view of the water.

Thank you Suki and TC for the advice! I will be sure to look into your recommendations. CJean and Noelle, thank you for the tip about Cruise Critic. I had no idea such a site existed!