What's Good In New York City?

I need some help.  Chris celebrated his 10 year anniversary at his job and his company gives a 10 year gift of a weekend in NYC.  We will leave Friday morning and come home Sunday afternoon/evening.  It's real fast, but they pay for all of our expenses, cab fairs, meals, hotels, plane tickets, and encourage us "to have a fine dining experience both Friday and Saturday evening", plus they pay for us to go to a Broadway musical, I'm hoping we get tickets to The Lion King

So what are the best things to do in NY in 2 days?  I've googled a ton of stuff and most say the same stuff, Empire State Building, Statue of Liberty, etc.  The only thing that I for sure want do do is the American Museum of Natural History and see the dinosaur fossils and then drift from there.

What's really worth my time?  A lot of people say the high line park, but I can walk around a park here, so I am not sure what I think about that or Central Park.  I'm interested in walking around China town but should that be a priority of other things?  Are the Brooklyn Bridge, Empire State Building and Grand Central Station as amazing as everyone says?  The weekend I am thinking of falls on the Cherry Blossom Festival at one of their parks.  Anyone know anything about this?

I'm not interested in shopping, I want to see things.  And what do you suppose "fine dining experience" means.  Cause I've googled some of the restaurants and we can have a 6-8 course meal at some Michelin star restaurants to the tune of $400.  But that seems excessive.   We definitely don't want to take advantage but I feel like something more then Olive Garden would be fine dining, and you can easily spend $50-70 there for two people.  I am trying to push Chris to get some more idea of what they mean.

And what about the World Trade Center Memorial?  I can't decide if it's something I would want to see.  What's there and am I going to just cry the whole time, because I would rather not spend the weekend crying.

I'm actually fairly excited about it, although it's still several months away.  We don't really do trips like this where it's so expensive.  We spent 2 weeks in Montana but we had family there and didn't have to pay for lodging, always a large factor in our trip planning!

Anyway, hoping some of you have gone or have family who may know of the good stuff.  Cause we need tips!