No international schools in Crete, so far. Only in Athens. Your children would be entitled to the Golden Visa and therefore they can attend any school .
What is the Greek education system like?
I want to buy a home on the island of Crete and will be bringing my wife and two children. Are my children eligible to attend the local schools? My children know some English, but no Greek. Are there any international schools for them, or must they go to the public schools?
They can go to international schools. No restrictions.
According to Greek immigration law, the holders of resident permits have access to public education, analogously to that of Greeks. But of course, they can also attend international schools too. If you are thinking of moving to Crete with children, their education will be an important factor affecting you decision of whether or not to move. There is one full-time school in Heraklion (a European school, nonfee-paying) that teaches lessons in English and two full-time private (fee-paying) schools in Chania that follow the American curriculum.