I read about this building in some material (I'm not 100% sure about the name, but the word "American" is surely included). It was one of the designs of a competition hold in the 30's. It had SEVERAL towers of different styles, like Gothic and Renaissance. It just looks like the castle in story books!
I think you may be talking about the American Standard Building at 40W 40th. Formerly known as the American Radiator Building, it was completed in 1924 by Hood & Fouilhoux. It is 23 stories (343') tall according to the 1925 edition of the World Almanac. The building has been made famous by numerous black and white photos and a painting in 1927 by Georgia O'Keefe simply called "Radiator Building - Night New York". Whether or not it was the product of a competition, I'm not sure, but Raymond Hood did win a competition two years previous for the Chicago Tribune Building (435 N. Michigan Avenue in Chicago). Both buildings are of the Gothic style. In the book, New York 1930, Stern Gillmartin & Mellins write that The stepped form of the Radiator Building was inspired by E. Saarinen's 2nd place prize design for the Chicago Tribune Competition. Hmmm....
I just reread your "question" and apparently I skipped over the part abour the SEVERAL BUILDINGS and the part about done in the 30's. That would more accurately describe Rockefeller Center. Our fella Raymond Hood was also involved in this project. There aren't any buildings in the complex with the word "American" overtly used in their name, but the RCA building could be the "Recording Company of America Building" in some print. Furthermore, the complex borders on the Avenue of the Americas.... These buildings are far less gothic inspired than the American Standard Building, however, perhaps in massing only. The predominant style would be an early modern (moderne, if you will) and mixes Art Deco details.