Most of our Pheasants here are stocked birds but they are still a lot of fun to hunt. They are farm raised then released on state owned land to be hunted.
We use to have some pretty good Grouse and Quail numbers in Connecticut as well but they are both pretty hard to find these days.

Some parts of the state also have a some Chukar Partridge that I have been told were used on a private hunting preserve but then escaped and have bred wild in pretty large numbers. I have yet to see one but a friend is supposed to be bringing me to spot that has some next week.
My favorite place to hunt has been up in northern Maine for ruffed grouse. It's about a 9 hour drive from me but it is well worth it in my opinion. I try to get up there for one week every fall.

That must drive you crazy to have wild pheasants out back and not be able to get after them!!