I have 10 days without plans from September 11 - 21.
I'll be coming into JFK and flying back out of JFK.

I would like to spend those 10 days in a tranquil area amidst nature around to go for a walk or hike, in a clean, luxurious, quiet 4 to 5 star hotel or something equivalent in terms of comfort and amenities. It needs to have decent Internet, rooms or suites with windows that open or even a balcony, a view of nature (not a parking garage, highway, loading dock or wall), modern bathrooms ideally, not the shower curtain style.
There must not be noise in the room, outside of the room, no highway or other busy road in front of the hotel, no weddings, conventions, retreats or similar noisy events. No construction site outside, no screaming drug addicts and EMS vehicles at night, no repair works in adjacent rooms, no noisy air-conditioning that needs to be running all night.

So I'm looking to sleep with the windows open and I'll hear nothing but birds singing, crickets chirping and rustling leaves, if at all.

Where would I need to go?

I don't want to add more flights out of NYC if at all possible, that's why I am looking for something close to NYC. I had enough trouble with US domestic flights in the past months and when I arrive at JFK I will have spent close to 48 hours on planes and in airports already and will just want to sleep without noise.

I don't need more Hyatt nights this year, have Marriott Platinum status and could use Marriott nights, but also willing to try something else altogether.