Two treasures of New York City can be found at this location (but neither is the cache).
The first is a memorial to the 26th President of the United States and former New Yorker (from Long Island): President Theodore Roosevelt.
The second is a magnificent tribute to the natural sciences and a gift to all children with curious minds: American Museum of Natural History.
President Roosevelt was a dedicated naturalist and a great friend of the American Museum of Natural History. In fact, Theodore Roosevelt Sr., the President's father, helped found the Museum. The following is a sample of quotations inscribed inside the Roosevelt Memorial rotunda at the Museum:
“There are no words that can tell the hidden spirit of the wilderness, that can reveal its mystery, its melancholy and its charm.”
“Courage, hard work, self-mastery, and intelligent effort are all essential to successful life.”
“If I must choose between righteousness and peace, I choose righteousness.”
"It is hard to fail, but it is worse never to have tried to succeed."
Clearly President Roosevelt is guarding the doors of the Museum and welcoming its visitors. But he is also standing watch over this cache. At approximately 330 feet from this spot, in the direction of the President’s gaze, you will be in the area of the cache hiding spot.
I hope you are as resolved as President Roosevelt was known to be on occasion.
Hints make it progressively easier...