Well, maybe it's not secret, or at least its existence isn't, but I reckon not many New Yorkers, and surely very few out-of-towners venture out to Corona Park in Flushing Meadows, Queens.
The secret part is that most anyone who hasn't been there isn't aware of the neat stuff that's there. Frinst, leftovers of two World's Fairs; 1939 and 1964.
The 1939 World's Fair leaves its legacy of the main building in the centre of the park, The New York City Building, which houses the Queens Museum of Art, with old souvenirs and scale models of the Fair on display, as well as a mostly modern art collection.
1964's Fair leaves us even cooler stuff. Old rockets (real and fake). The Unisphere, (featured in the hit crappy movie Men in Black, oh I guess maybe it's not terribly secret) a 300-ton stainless steel globe that stands 140 feet tall. The Unisphere is actually made of a bunch of rings, it doesn't have a covering, so if you were a really good climber you might be able to climb up the inside of it. But you'd need some strong magnets or something I think. You can also see various weird sculpture from 1964 such as Donald DeLue's 45-foot "Rocket Thrower" and Marshall Fredericks' "Freedom of the Human Spirit."
I save the best attraction of all for last: 1964's "Panorama of the City of New York" in the Queens Museum of Art. This, the largest architectural scale model ever created, replicates all 5 boroughs at a scale of one inch to 100 feet. It took 20 workers two years to build (assuming 40 hrs/week, 50 wks/year, that comes to a staggering 40,000 man/hours!). The model contains 835,000 miniature buildings, 35 bridges and 2,500 lights, which turn on for the Panorama's simulated night, which falls every eight minutes. 1964 Fair-goers actually waited in line up to an hour and a half to ride over the "city" in a "helicopter" cart hanging from a track in the ceiling!
Add to these wonderful spectacles the fact that the park isn't terribly popular and that it is nice and big (bigger than Central Park!) and bring a picnic lunch and it's well worth the 45-minute ride on the subway from Manhattan.