Middle Eastern Food outside of Stamford
There are some places in Bridgeport but I don't think you would like them.
If you were willing to drive 20 minutes farther to Waterbury there is a Turkish place that has been getting some love from chowhound.
Anatolia Restaurant - 586 Plank Road - Waterbury
This is a bit out of your bounds, but Hanna's in Danbury is good. Authentic food and the portions are pretty generous. There is a small store next door owned by the same people (it started out as a store many years ago...) and you can pick up many Middle Eastern spices and foodstuffs there.