B.E.
I'm no longer in NYC, but we just visited two weeks ago and went to the Transit Museum in Brooklyn - it was really cute and the kids seemed to be having fun. I've also heard that one of the upper floors of the Natural History Museum has some great interactive activities for kids. Not sure which floor - sorry! Of course, Central Park Zoo before it gets too cold. Even the Metropolitan Museum can be a fun place for kids, in small doses.
I've always heard the 92nd Street Y offers all kinds of programs. She should also check into Chelsea Piers and see what kind of programs they offer for kids.
No clue on the preschool - sorry. That's why I left! :)