To what civilized people does Odyssues tell the story of his wanderings in The Odyssey?

Odysseus tells the epic tale of his wanderings to the Phaeacians. He is the honored guest of their king, Alcinous, who invites Odysseus to a sumptuous feast in celebration of the sea-god Poseidon (who, it has to be said, isn't Odysseus's favorite god. After all, he wouldn't have winded up in Phaeacia had it not been for Poseidon's ruthless vengeance).
The Phaeacians are indeed a civilized people, but they also have a reputation for being a tad xenophobic—that is to say, they have an irrational hatred of foreigners. That's why Odysseus's divine protector, the goddess Athena, shrouds him in a magical mist that protects him from being harassed. The implication here is that most visitors to this kingdom tend not to be hospitably received.
Even though the Phaeacians break their normal habits and show Odysseus the hospitality to which he's entitled, our hero still doesn't relax completely in their presence. Nor does he reveal his true identity as he recounts his epic tale. Even so, King Alcinous knows there's something special about his honored guest. He's so impressed by Odysseus that he graciously offers him his daughter's hand in marriage. For obvious reasons, however, Odysseus must politely decline.