Where did Miyax's father live at the end of the book Julie of the Wolves?

The simple answer to your question is that Miyax's father, Kapugen, lives in the town of Kangik at the end of the novel. The longer answer to your question involves Kapugen's history with his daugher, Miyax.  

During her early life, after Miyax lost her mother at age four, Kapugen took Miyax to live in a seal camp near the Alaskan village of Mekoryuk.  It is here that Miyax learned all of the "old ways."  It is...

The simple answer to your question is that Miyax's father, Kapugen, lives in the town of Kangik at the end of the novel. The longer answer to your question involves Kapugen's history with his daugher, Miyax.  

During her early life, after Miyax lost her mother at age four, Kapugen took Miyax to live in a seal camp near the Alaskan village of Mekoryuk.  It is here that Miyax learned all of the "old ways."  It is only when Aunt Martha arrives and yells at Kapugen for not sending Miyax to school that he sends her away.  Eventually, at age thirteen, Miyax escapes from her Aunt Martha by agreeing to an arranged marriage.  Miyax escapes from the arranged marriage by fleeing onto the Alaskan tundra and becoming a member of the wolf pack.

At the end of the story, a citizen of Kangik comes by Miyax's dwelling and lets Miyax know that "the greatest of all living Eskimo hunters" lives in his village. Miyax knows this is her father, Kapugen.  Unfortunately, Miyax discovers that Kapugen has abandoned many of the old ways.  He has married a white woman and is living with many modern conveniences.  Worst of all, his job is to fly hunters over their targets by plane.  This is how Amaroq was killed.  This realization makes her father, Kapugen, become "dead to her" and forces Miyax to admit that the "the hour of the wolf and the Eskimo is over."