If you're looking for authentic, family style Middle Eastern food and market, I think you're going to have a hard time finding better than The Olive Tree.
It's run by a Jordanian family that couldn't be nicer or more on top of their food game. They're making cheeses, curing olives, baking baklava...all the good stuff you want from a specialty market. The market itself is clean, well stocked and appears to have solid turnaround on their products.
The grill can't be beat...the best kebab I've had (in the US). Everything is super fresh and made to order. The tabouli is awesome! Get the combo plate - choice of any three meats with basmati rice, salad, pita and garlic sauce. The breakfast options are great too, for all you early birds.
Stop searching for good Greek/Mid-East/Kebab, you've found the right place!