Since classical period antiquities are the same in Greece and Italy, I would suggest that you visited Crete and Santorini. They are both beautiful and interesting islands. On Crete you can visit Knossos and Phaestos with the wonderful palaces, the famous Labyrith (Maze) of Minotaure and the remnants of the Minoic Civilisation, so you should add Herakleion in your list. On Santorini (or Thira) you can combine the visit of the pre-historic site of Akrotiri where you can see a reconstructed city together with the visit of an actual volcanic island where Geology meets History, Winery and Romance. If you want to save time, both islands have international airports with many incoming charter flights, especially in holiday season. If your program does not allow you visiting the islands, you can always visit Athens where there are plenty of museums covering the whole Greek History, starting from pre-histoy, classic years, prime and post byzantine and coming up to the contemporary days.
Whatever you decide to do, wish you to have fun!
10 days is hardly enough to get more than just a glimpse at both .
I'd say your choice is basically Rome and Athens .
You could squeeze in a visit to Aegina island just across the Saronic Gulf from Athens which despite it's proximity ( an hour's run on frequent daily boats) has a true Greek-Island feel to it , but thats two more half-days of travel
A place that will cover all of you in that short time will be Heraklion Crete, where Knossos and Phaistos or Festos are located and a newly restored museum holds a treasure of artifacts from the whole island. At the same time there are many seaside resorts to spend good family time relaxing by the sea.
I don't have clue for Greece, but I recommend you to go to Rome and Florence. They're so worth visiting!
Since your kids love museums and stuff I think the best place to go would be in athens because there is sooo much history/museums/ruins/etc. But, Santorini is SOO gorgeous!! And I'm sure they have museums there too but there is more stuff in Athens. No matter where you go in Greece im sure you will love it!! One trip I'm sure will not be enough! ?????? Have fun!!