Given Odysseus' criticism of the Cyclopes, what kind of society do you think the Greeks valued?
This is a great question, because it shows that you have a great eye for historical and social detail.
First, we should give a summary about what Odysseus thought about the Cyclopes. In short, according to Odysseus, this race of one-eyed giants was barbaric. Polyphemus and the other giants had no laws, no councils, and no traditions of civility or hospitality. Luckily for them, they lived in a fertile place that did not need to be cultivated. When Odysseus tried to see if these creatures would show hospitality, which was expected, he entered into a mess, where a number of his men were eaten.
Based on these criticisms, it is clear what virtues the Greeks valued. The Greeks valued elements of society that would create a strong polis (city), such as laws, councils, and other civic activities. If we think about the Athenians and Spartans, it is clear that they valued laws. All we need to think about is Solon and Lycurgus (the great lawgivers of Athens and Sparta). Also if we look at the traditions among the Greeks, such as the great religious festivals and games (the Olympic, Nemean, Corinthian and Pythian Games), it is clear that the Greeks prized city life.
Finally, the Greeks valued hospitality. This is why Odysseus actually stayed. He expected Polyphemus to be hospitable. When Odysseus was given nothing, he could only say that they were barbarians.