My concept includes the spires of the Chrysler Building and the Empire State Building for the top of the cake. Using these iconic buildings in the logo identifies your location without the use of the academy's name. I feel these would work for NY Cake as a simple cake silhouette but with the addition of decorative elements, can represent the academy as well. Also, I think it would be a great idea to incorporate French art deco elements if you go with the Chrysler. Since Art Deco was about ornamentation, it's ideal for this application.
If you like this direction, I'd be happy to make any revisions. Your feedback is welcome. Thank You