The best part of Middle-eastern stores is that most of them have a butcher on the premises, who, often will be able to customize cuts of meat that are virtually impossible to find in a conventional supermarket. I go to these Halal meat shops for fresh and reasonably priced lamb and goat meat. For instance, they sell a whole leg of lamb and upon request (at no extra charge) they de-bone and butterfly the entire leg for me.
I also buy Turkish coffee, favored teas, dried fruit, couscous, olives and feta cheese. I also get specialty ingredients such as tahini paste, jarred grape leaves, Zataar, Labneh and Sumac there.