Any suggestions on "special" places to go with my daughter? Would like her to experience something "really neat", in addition to shopping, broadway & museums.
Any place special to eat that would be interesting to her?

Valerie, what are her likes and dislikes...how does she prefer to dress...and, is she sophisticated, etc.?

If she likes jewelry, try roaming around the Diamond exchange area. Lower East side for shopping and historical perspective, Canal Street for knockoffs, Greenwich Village just for, a walk across the Brooklyn Bridge, a trip into Brookklyn if you have time, horse and carriage ride around Central Park. Afternoon Tea? A haircut and/or manicure at a great salon? Merilee hit it on the head. What does she like.

Afternoon tea at the Plaza Hotel is quite an experience. How about a half day at a spa? Bliss is best but book early.

When you go shopping, spend some time in Bloomingdale's, then go around the corner and eat at Serendipity 3 (East 60 St.). The recent movie of the same name took place there. It's fun!