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I did this almost exact same itinerary but from yvr to jfk on cx, but the concept is the same.
I've been to nyc once before so it all made a little more sense to me. A few pointers I'd have is:
The stored luggage place is slow as molasses. There is literally one guy at a hole in the wall in terminal 4 that does this. Cash only of course as well so be ready.
Taking the subway into the city is actually quicker than a taxi in my opinion. No traffic to deal with, and a heck of a lot cheaper.
In my one day, I did a walking/bike tour through central Park that spanned about 2 hours. Grabbed some lunch at some random places the guide recommended nearby to the park.
Headed over to Brooklyn on the subway then walked over the bridge back into Manhattan with an awesome view. Walked over to the 9/11 memorial. Finished it all of with some power shopping at century 21 before schlepping back to the airport to grab luggage at t4. If you plan it out, should be able to accomplish quite a lot.
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