Seattle has an excellent Middle Eastern restaurant at 408 Broadway E on Capitol Hill, phone (206) 860-6826
Ali Baba, sub-genre Palestinian/Jordanian. It is very very good, better than what is typically available even in NY. I'd suggest eating vegetarian your first few times to appreciate the way the food is eaten authentically. Just get sides of tabouleh, hummus, baba ganoujh, foule, and felafel, and they'll come with bread, dip in. (The tasty foule is especially good for beginners; the real thing can often smell sewery.)
I think it is better even than the storied Omar al Khayam in Renton, and a lot more convenient.