What are examples of Greek values shown in the Odyssey besides hospitality and family values?
I would say that one of the most striking example of Greek values displayed in Homer's work comes when Odysseus tours the underworld. The Greek value of honoring the dead as well as the immense respect that the Greek culture had towards the human soul comes out in this instant. Odysseus travels through the underworld and does not silence the voices of the dead that inhabit it. Homer is able to construct a setting in which Odysseus acknowledges a form of reverential debt that the dead have paid in order for Odysseus to be in the land of the living. When Odysseus listens to the different stories of the different souls in the underworld, it highlights the Greek value of respecting the dead. Odysseus does this in Book XI in his tours of the underworld. At the same time, I think that Odysseus' experience highlights the Greek value of the immortality of the soul. The dead are not really "dead" in the traditional sense. Achilles embraces this as he gives his own opinion of mortality to Odysseus as one in which life, in whatever form, is to be revered. Hearing this from one who has passed into another realm is another form of respecting the dead and the notion of the soul's immortality. Both Greek values are present in the moment in which Odysseus voyages through the Underworld.
Another one is arete, which means to strive for excellence. Although this value is much more prevalent in the Iliad, it does show up in the Odyssey, mostly in the form of people telling stories about the Trojan War. It is the thing that heroes must strive for in order to become famous.