Where is Rainy Mountain? Why does Momaday return there?

A close reading of the narrative answers these questions. Here's the passage:

A single knoll rises out of the plain in Oklahoma, north and west of the Wichita Range. For my people, the Kiowas, it is an old landmark, and they gave it the name Rainy Mountain.

The Wichita Range is a mountain range located in southwestern Oklahoma.  Momaday also explains why he returned:

I returned to Rainy Mountain in July. My grandmother had died in the spring, and I wanted to be at her grave.

Momaday's journey is a personal journey. He goes home out of love and respect for his grandmother. He wants to visit her grave, grieve her loss, and honor her memory. Also, by going home he returns to his own cultural roots and embraces his heritage.