This must be a branch of the Zeytin on 85th and Columbus (or vice versa). Glad to hear they have another branch, because I think their Columbus Av. branch is threatened by proximity to Kefi. How do the branches compare in size and food quality?
The spelling is actually Zeytinz and it's more of a market than a sit-down restaurant. I don't think it's related to the Turkish restaurant on the UWS, rather I believe they're related to the Zeytuna grocery stores in the Financial District.