Spend a day or half a day in Central Park – the skateboarders, the cyclists, the zoo, the boat pond are all delightful and most of it is as it was when Olmstead and Calvert designed it. You can combine that with a visit to the MET. Circle Line around Manhattan or a Grayline sightseeing bus from the top deck. Oh – try to get to Marie’s Crisis in the Village – it’s a tiny little bar in the Village where professional actors and amateurs (many gay) sing Broadway songs around a piano. Late at night is best there.
If you want a splurge, an elegant afternoon tea can be had at the Lowell Hotel on the East Side.
For theater, my cousin said “In Transit” is delightful at the Circle in the Square and shouldn’t be hard to get tickets to. “Avenue Q” is also great if still around and your daughter would love it too. I’m also planning to see “Indecent” and “The Play that Went Wrong” later this spring.
The Morgan Library is great and a short visit is fine. Nice cafe there too.
The Highline is fun – although I don’t like it as much as others do – for walking with the Whitney at the end.
Lastly, maybe have brunch with some friends.