It goes by many names -- different signs and flyers carry various names -- but in terms of Middle Eastern and halal food, no store in Spokane does it better than the International Food Store.
The selection here is pretty outstanding, and if you have any interest in authentic hummos tahini, Ziyad's canned stuff is probably better even than anything you can make yourself. There's a good choice of different types of pitas too, again all of high quality.
More important, to me at least, is the choice of "Greek" yoghurt. I use quotations around "Greek" as that's actually a common misnomer. Strained yoghurt -- which is what we call "Greek" here in the US -- has its origins in the Middle East. Traditional Greek yoghurt is not strained. Therefore "strained" yoghurt would be a better name for it.
International Food Store carries multiple brands of the extremely flavorful and fatty yoghurt and, as you only need to use a dollop of it while cooking, a container goes a long way. (And you will never ever again use what Yoplait calls Greek yoghurt.)
They also carry hookahs ranging from $20 into the hundreds.
We like international markets quite a bit here at Team SpoCOOL, and International Food Store is one of the more interesting ones in town. A must if you are interested in Middle Eastern food.