At the time of this writing, Balkanika is virtually nonexistent in cyberspace (save for this blog post). It opened the Friday of Memorial Weekend and I visited for the first time just a few days ago. The market area at the entrance of the restaurant has fresh fruit and vegetables, whole coffee beans, crackers and other groceries plus a cold food bar. The restaurant begins further in, serving a collection of what I can only describe as "Mediterranean" food. Drinks include hot or iced coffee, wine, and beer.
The Village Voice and the listing on Chow say it is by the same owner as Kashkaval, which isn't hard to believe since Kashkaval is also a market/restaurant hybrid, albeit with a focus on wine and cheese. I had a pasticio, described as a Greek lasagna, and a friend ordered chicken pilav with rice. I'm not a food critic but I will say, I liked! And I will be back!