Does anyone remember the name of the magazine, which later became a supplement to New York Magazine?

It had restaurant and theater reviews, updated weekly? It wasn't Playbill or Howard Hillman's, it was something else; it became part of New York Magazine in the late 1970s/early 1980s. I think an older reader could answer this. Thank you.Does anyone remember the name of the magazine, which later became a supplement to New York Magazine?
Yes, I think it was called Variety.