I would look mainly for smaller independent luxury hotels and inns in the Poconos (northeastern Pennsylvania), Catskills (southeastern New York) and Berkshires (western Massachusetts), all of which are a roughly 2-4 hour drive from the city (a bit more from JFK if there is traffic). I've only stayed in low-end accommodations in those regions, which wouldn't meet your requirements. But there are lots of small (and probably some medium-large) independent inns and hotels that I suspect would be a great match for what you're looking for. The only challenge, as travelingdrsuz said, is that you'll almost certainly need a rental car (or an expensive chauffeured ride) to get there.

Here are a few lists that have some promising leads:
https://www.cntraveler.com/gallery/b...tskills-hotels
https://www.travelandleisure.com/hot...r-editors-love
https://www.architecturaldigest.com/...hotels-to-book