Welcome to TUG. I see this was your 1st post. There have been many discussions about Greece in the 'Travel' section. Feel free to use the search function. I also use www.frommers.com where there is a very active community of travelers and wide ranging, area specific topics.
If this is to be your first trip to Greece, you may want to go to a nearby book store and peruse the many guidebooks available. You'll want to have one of these with you anyway. If this is a timeshare trip, you may want use your membership (thanks!) to get access to the resort reviews.
Good luck, and again, welcome to TUG.
Oh, and we enjoy Rhoades, away from town. Mykonos better than Santorini, Athens is good for a couple of days but not much more.
If this is a once-per-lifetime trip you must see Santorini.
Santorini is a long ferry ride from Athens and a short ferry ride from Crete. It's also reachable by air from Athens (as is Crete).
Crete being the largest and sourthernmost Greek island is more like a small country. It has some wonderful beaches and also great culture and quality of life, and has not been destroyed by tourism the way some small islands have been.
So one possible itinerary would be
-- fly U.S. to Athens to Crete, stay five to seven days in Crete (jet-lag wipes out the first day; and you need a car to get around), then
--ferry to Santorini, stay two to four days, then
-- either ferry from Santorini to Mykonos and stay two to three days before flying to Athens, or fly directly from Santorini to Athens
-- stay two days in Athens before flying home (you've got to see the Acropolis and the National Museum)
The real beauty of Greece is the islands, but you should at least see some of the mainland and its antiquites. There is not much in Athens other than the Acropolis and the museums. The Plaka is a good place to do some shopping. It is next to the Acropolis. Whilst in Athens you can see the Temple of Poisdon and Delphi.
The Peloponnese area is nice and we really enjoyed Olympia, the site of the first Olympic Games. It is interesting, because some of it still there.
There are one day junkets out of Athens that take you to Hydra, Paros, and one other island.
Northern Greece is also fun to see. It is very wooded and green. Reminded me of the Black Hills, without the taller mountains. We took a car tour out of Thessaloniki. Lots of little costal fishing villages to visit.
Off the coast of Volos, is the island of Skiathos. As contrasted to many of the Greek islands, it is green and heavily wooded. This is the island where they filmed "Mamma Mia.":whoopie:
The best time to go to Greece is the first part of September; August is a disaster. In September the weather is still good, everything is still open, and the European tourists have gone home.