Rent a car and drive upstate. There is more and more to experience in the Hudson Valley. In the summer, Montauk.
Things to try: Gaskins restaurant in Germantown (I am still dreaming of the apple and celery salad they served as an appetizer, and the young ginger ice cream for dessert), River Town Lodge hotel in Hudson. (There is also an impressive selection of design and antique stores on the main shopping street of Hudson.) Table on Ten for pizza and why not stay there too, if you able to get a room. (The weekends are busy, so book well in advance.)
Driving around and seeing the state from a broader perspective – the empty lands, the rugged old cabins with a tv and plastic chairs on the porch, the silence, along with the beautiful nature, the new wave of organic farming and the abundance of newborn small local companies – you understand what drives people to New York City, and what drives them out here.