Where would you take your family of 4 on vacation just outside of NYC for under $1,000?

We want to take the kids away for a few days in July. We are a family of 4. I was thinking of cabin camping, but we are open to something else.

Where are your favorite just outside of the city mini vacation places?

Edit: We have do have a car. We are pretty easy people as far as having fun. We enjoy being outside, so any hiking, beaches or parks are good. We like sightseeing, so museums, boat rides or walking tours would be cool. The kids are going to be 8 and 10, they like to try new foods. We love street fairs and festivals.