Never been to the one in the city, but the one up in Tarrytown is fantastic. Though I don't recognize anything specifically on the menu you linked, my general recommendations would be that all of the salad's I've had there are surprisingly good, and their cheese plate is distinctive.
I don't know if they do it at the new york one, but the other one does a "Farmer's Feast" prix fixe menu which is a always great selection.
the berkshire pork is really good.
i LOVEd the salted caramel ice cream that comes with the chocolate bread pudding but the actual bread pudding was not my favorite. it was three little glistening cylinders of very spongy cake and a funny flavor that i can't place. still, i think it's worth it for the ice cream because it is that delicious.
my mom loved the berry coupe.