Does where you live affect the phase of the moon you see?

No.

There are phases because only half of the moon is ever lit by the Sun (the Moon doesn't rotate, so it's always the same half that faces Earth but different halves are illuminated due to the orbit of the Moon around the Earth), and as it orbits the Earth, we can see different parts of the illuminated section.

Everyone that can see the Moon at a single moment in time sees almost exactly the same phase.There could be a slight difference due to observers looking at the Moon rising and setting from different parts of the Earth separated by the Earth's diameter. This provides a difference and that difference is so slight that it takes a very good telescope indeed to note it.

See related link.