I went to a Mideastern takeout establishment in Great Neck (Middle Neck Road) called Amal .
They had a few stools and a counter top, where you could eat. The menu was much more extensive than a typical "Israeli" type of eatery. They had selections from Iraqi, Morrocan, Persian, and other Mizrachi type of food. I had their schwarma as well as their Iraqui Kabob. The owner was very friendly and showed me their homemade extensive Mizrach frozen food selection in their freezer case.
I would recommend getting food from Amal if you are in the area (near Great Neck Glatt & Chosen). My selections were good and the falafel sample and pastry sample that I had were also good tasting. By the way, they are under Vaad of Queens supervision.