I like history as a side interest/hobby, and historical fiction is my favorite genre of fiction, but I have trouble finding good ones that did not take place in the west (Europe/North America). For example, here the top suggestions are Patrick O'Brien and Bernard Cornwell's works, which are excellent but all happen in the West, portray the western culture, etc.
Any good books with other backgrounds? e.g. Middle East, East Asia?
You could read the Romance of the Three Kingdoms and Water Margin, they're sort of like the Chinese version of the Odyssey and Iliad except in prose.
As for an American historical fiction novel there's Shogun by James Clavell and its sequels
For non-East Asian history I'm not so sure, you could read 1001 Nights for the Middle East if that counts.
Actually, here's a wikipedia article with a list