I would think happy valley and little John get stockings. Its pretty decent small game lands and one reason I'd like to own a peice of Oswego county

I don't think there is any of the kind of habitat pheasants like in Little John, between the mature forest and the deep snows of winter, but Happy Valley has lots of cattail marsh where they can get under something and not freeze to the ground, and there is a lot of cropping going on, so they can find grains.  Altmar State Forest is not far from Parish either, and has some of that edge cover common in Happy Valley.
 
IF they were meant to be here the pheasants would be thriving.  Another exotic species introduction that fails with a change in  agricultural practice, or a slight shift in climate.

With all the cornfield habitat surrounding, I'm pretty sure they are around up there.

Believe it or not there used to be a good population of pheasants in the greenbelts along the parkways in lower Westchester County, NY.  There was a spot at the intersection of the Saw Mill River & Cross County Parkway's in Yonkers, a few miles north of the NYC line. While working midnight's I would watch hen's and their poults fly down at first light.  It was comical to watch the cascade of poults as they clumsily dropped from their roost.

I'm up in that area a LOT in the spring and summer.  There are no farms right around Little John, and mostly pasture in the nearby ones.  You are almost to Lacona on County RT 15 before you see any corn stubble in the fields, and onto the lake plain before you hit the big dairies that grow a lot of feed corn.  Grouse and Snowshoes, and the grouse are way down and the bunnies have been scarce for a while.  As many say here, too many 'yotes. 

West Nile disease has been linked to the ruffed grouse decline. 
This fall I hunted on a nearby piece of state land on the NY/CT border that is a mix of hardwoods and fallow fields.  While there I ran into state biologists who had set up bunny traps for a study.  It will be interesting to see the results of that study.

I've never explored any of those management areas so I can't speak from experience. They are on my bucket list of short trips with lots time on my side.
Just figured given the vast sizes and horse and buggy near by there's got to be some habitat surrounding.

A friend of mine went pheasant hunting on a private preserve 2 days ago. They had a blast and took many photos of birds of pay.
Not really my idea of fun stuff

I've been to Orvis Sandanona which is less than an hour from my front door.  It's a beautiful piece of property but well above my pay grade.  Lol
The only times I've frequented that establishment was to buy fly fishing items in the Orvis shop. 
I do know guys have hunted woodcock on the 700 acres of watershed property 300 yards from my front door.  They don't get many but birds are there.  I haven't seen or heard any honkers (ditch chickens) or grouse while walking the property.  

This is a pay to play place near Westchester co.
Not my digs to set birds and let dog flush ditch chickens.

At nearly 60 degrees out its mud season.
Spending the day inside doing pinewood derby projects with the grandkids.
They race next weekend.
In past 2 years my oldest cub scout has been progressing further.
Year 1 = 3rd
Year 2 = 2nd
We are hoping for gold this year.

My newest cub scout is in his first race