This could have replaced Grand Central Station:

From the New York Times:

As pressure to use the air rights above Grand Central Station mounted, developers tried time and again to propose lofty alternatives. The gutsiest was I.M. Pei’s Hyperboloid, sponsored by the developer William Zeckendorf, in 1956.

The hourglass-shaped design, whose altitude would have surpassed that of the Empire State Building, was light years ahead of its time, incorporating a weblike steel exoskeleton to support the open floors within. Squint and you’d think you were in Dubai, 2016.

There are nine more of these could-have-beens in this article, with some classics like Robert Moses proposal for a road through Washington Square Park (he didn’t count on Jane Jacobs and friends), and some unexpected ones even New Yorkophiles may not have seen.