Depends on what your into. Definately do the big sites, I lived in and near NYC for years and never bothered, then finally was talked into it and really enjoyed it.
Then if you want to get some NY feel.
- See a Yankees game.
- Go to St. Nick's pub in Harlem for Jazz on a Monday or Friday night (try and go with someone who knows NY tho as Harlem should be respected; particularly those unfamilure)
- Wander in the villiage and Chinatown
- Do "Museum Mile" along Central Park, particularly the American History Museum.
- Go to the Cloisters in Way upper Manhattan
- Go to Jones Beach or Coney Island
- Go to Times Square and Toys R US
- spend a day at the Brooklyn Botanical Garden and Brooklyn Museum of Art (they are next to each other)
- Pick up a copy of the New Yorker and spend a day at the Gugenheim (sp?) then go to an OFF-Bradway or broadway show ("The Goat" or "The Guys" or "QED" are nice) then go to Bleeker street for a late dinner (Johns Pizza or the Mona Lisa Cafe are personal faves), then walk around for a bit to work off dinner. Then go to get dessert at Rocco's or Bruno's or if cake and cookies is your gig then Magnolia is the place to be. Then head for a Bleeker st. club or bar for a nice buzz (asylum is cool for a good chill). Then head for Small's to chill the rest of the night to some great Jazz. (small's is open untill 8AM or something if your up to the task, they are BYOB tho...)
This could go on and on... and depends on your tastes - but have fun!
ps - get a good tour book and map with subways.
edit - i just noticed the family oriented part - you might want to drop off the kids between dessert and the bar