Re: Non-Western Mythology Based Fantasy novels......
Most of what I was planning to suggest has already been mentioned. As such, I'm going to briefly second Tales of the Otori, Journey To the West, and The Epic of Gilgamesh, as well as the works of Nnedi Okorafor. In addition to that, there are a few other possibilities:
Under Heaven - It's set in what is a very obvious fantasy analog of Tang China, and is a fairly good book. The author is the Canadian Guy Gavriel Kay however.
The Lions of Al-Rassan - By the same author as Under Heaven, the Lions of Al-Rassan is set in what is clearly reconquista Spain. Strictly speaking that is in the west, but it isn't entirely culturally western at all.
The Journey of the Catechist - This is a fantasy adventure story set in fantasy-Africa, written by one Alan Dean Foster. It's unconventional in some ways, but is generally good writing, and it has the Nnedi Okorafor seal of approval.
Fudge Assistant in the Playground.