One of the mythical Ionian islands, Zakynthos (also known as Zante) is second only to Corfu in popularity for Greek family holidays, and child-friendly accommodation is plentiful. It's a great destination with kids, although you need to be careful where you pick as a quick buck was prioritised over quality when most development took place here. It's also best to come in spring, when you can avoid the scorching sun and there are less people.
You'll find Zakynthos a beautiful, lush island once you start exploring. Keep the kids happy with watersports and island hopping and keep yourselves happy by sampling some of the great local cuisine. The island has been conquered by a dazzling number of civilisations, all of whom left something of their culture and architecture behind.