Westchester/Putnam doesn't have a large amount of public access courses, so i dont know if you would consider them hidden gems, but perhaps not on the radar of the casual golfer. Definitely worth a look though.
Harlem Valley Golf Course - Wingdale, NY. Donald Ross supposidly designed it in 1928
West Point Golf Course - Has some interesting holes and great views.
Sedgewood Club - Carmel, NY - Way up on the middle of no where on the smallest dirt road, they might have 50 members, very interesting place.
Quaker Hill - RTJ 9 holer in Pawling, NY
Red Hook Golf Course - Red Hook, NY - Unfortunately they threw some awful condos on the first couple holes, but after that its nice. Back nine is above average with some really interesting holes cut out of some pretty dense woods. Often overlooked in the slew of public courses in Dutchess (James Baird, Union Vale, Casperkill, Carvel, Silo Ridge, McCann).
Buffalo/Niagara region
Beaver Island State Park - Worth playing if you are in the area, not very difficult, but fairly scenic and a nice walk. It's in good shape for a state park