Some of the books recommended here, are set in non western world, but they are NOT High Fantasy. Not at all.
I recommend Fuyumi Ono's "Twelve kingdoms" [十二国記 in Japanese]. Tokyopop translated first 4 books in English, but there are fan translations online for the rest of the books. And if by any chance you read French, all are translated and published traditionally.
http://www.goodreads.com/series/4409...welve-kingdoms
Here's the setting of the books:
Spoiler:
The Twelve Kingdoms is a series of novels that focus on a world inspired by Chinese mythology, where twelve kingdoms exist under the rule of an individual chosen by the heavens. The series does not exclusively focus on one character, though the stories of Youko Nakajima, the protagonist of the first novel, and Taiki, the protagonist of the second book, are most prevalent in the series.The Twelve Kingdoms tells several stories from the world of the Twelve Kingdoms, located on several islands in another dimension accessible from our world through magic (though the other way around is normally impossible). On the islands, magic works and societies similar to classical China exist. While the inhabitants of the Twelve Kingdoms are aware of the existence of our world as the lands of Hourai (Japan) and Kunlun (China), the reverse is not true. The inhabitants of the kingdoms speak a different language than the language of our world, both of which can be learned by ether side. Only extraordinary circumstances can enable the two worlds to affect each other for certain periods of time.
In this world, there are a total of thirteen lands. At the center of the world lies the Koukai (the Yellow Sea) and Mt. Hou, where the Gods communicate their will to the twelve kingdoms of the world. Each of the Twelve Kingdoms possess their own ruler and its own Kirin, a divine creature which embodies the will of heaven and is entrusted to choose a kingdom's ruler. The ruler will have immortal life as long as he keeps the kingdom healthy and their heads are not severed from their body.