How can a family experience NYC in 2 days?

Ok, nobody can tackle this huge city in such a short time. Despite having grown up in Boston area my whole life, I’ve never been to NYC. I’ve never been interested in cities, so it’s never been a priority. Whenever I have found myself with a couple days off, I have always headed to the mountains.

My wife and I have decided that we need to stop avoiding NYC, and have decided that a free weekend in October may be a chance to go. We have low expectations, but are likely going to be going as a family (+ 3 kids). Our (overwhelming) goal right now is to just find some place to stay and a couple of things to see. We love to eat, so staying and being near good food would be important.

Any thoughts for a city-phobic NYC newbie and family? Any suggestions would be welcome.

If you were to go to only one museum, what would it be? Other sites? General areas to stay?