I have always used points for stays in NYC, so I can't comment on hotels, although the DoubleTree Times Square is in a perfect location.

Must sees? 9/11 memorial and Museum. MOMA, and the Met. Also look up the Frick Collection is pretty amazing as well.

Not into Art. McSorley's in the East Village is a riot, but maybe not for kids. just don't try to order anything other that Light, Dark or Jameisons.