The six-part documentary In Search of Troy by Michael Wood (may need some slight editing for children - mostly a piece of the introductory sequence to each episode) turned out to be an excellent introduction for all of us. It doesn' t overview all of ancient Greek history by any means, but visiting many of the archaeological sites and hearing stories about important people and places helped develop interest in the beginning and make connections as we proceeded to read various books.
My 6th grader enjoyed Hittite Warrior soon afterwards and understood it better than I had done when I read it a few years earlier - so many of the names and sites mentioned in there had come up in the documentary.
The 1st and 3rd graders also listened in on Black Ships Before Troy by Rosemary Sutcliff and the 6th grader followed it up with The Wanderings of Odysseus by the same author.
As a family we've been reading:
String Straightedge and Shadow: The Story of Geometry by Julia Diggins
This delightfully brings together threads about knowledge and learning in the Ancient World with a wonderful sense of the order and beauty of mathematics(haven't finished this one yet - there is one strange little thread about a secret society that might make some uncomfortable)
The Story of the Greeks by H.A. Guerber
Interesting and substantial overview of Ancient Greece for children (haven't finished this one either but I like it a lot. The piece on Sparta mentions infanticide - not approvingly, but still disturbing - that was practiced by the Ancient Greeks. Might be best as a read-aloud for younger children.)
Stories from Herodotus by Glanville Downey illustrated by Enrico Arno
We LOVED this one. Herodotus is so fascinating already (read him in college), but not suitable for children in length, complexity or some mature content. This edition brings together many of the most interesting stories (focusing on the Persian Wars and especially the battles of Marathon, Thermopylae and Salamis). To me this highlighted some of the best content about Ancient Greece for children. Even stories involving oracles and pagan gods provided thoughtful content for my children as there tended to be warnings about the arrogance of those seeking the gods' advice and confusion regarding its implementation. This again was a great read-aloud and we enjoyed discussing little tidbits - humorous, clever, etc. - along the way. We found this at our local library, it is currently out of print.
D'Aulaire's Book of Greek Myths - This seems to be universally considered the best introduction to Greek Mythology for children. Even my high school Latin students, who needed an overview of Mythology for the National Latin Exam this spring, used this book for a quick review. My husband read this aloud to the children at bedtime during our Greek study.
My 6th grader also read:
The Tale of Troy by Roger Lancelyn Green
Tales of the Greek Heroes by Roger Lancelyn Green
selections from All Ye Lands (Catholic Textbook Project) for a helpful overview/review of the time period.