I think that was a music pavilion after the World’s Fair. Led Zeppelin etc
That’s a shame.
It used to be mine as well, long before those structures were even dreamed of. I learned to ice skate in the NYC Building and how to swim at the Aquacade. Both of those sites were leftovers from the '39 Fair. My grandfather(who passed away in '50) used to take me mushroom hunting there. My mother learned how to drive on the winding roads in the "Fair Grounds" as it was known. (Can still hear my father yelling, "Clutch...clutch...clutch" as the car bucked and lugged) I learned how to fish there, an avocation that remains to this day.
Aside from sitting under the Unisphere, passing around a jug of wine, listening to the concerts in the NY State pavilion in the early 70's, I don't think I ever went back to the Fair Grounds for the rest of my time in Fun City.