I loved the Museum of Native American History, I could have stayed there all day, instead of the half a day we were there.
Definitely get the Staten Island Ferry, I couldn't believe it was free, but it's great for stop offs, including Ellis Island and Staten Island itself.
Last time we were there we stayed right next to Ground Zero, the time before that the Twin Towers were still in existence.
I love the Empire State and the Chrysler Buildings, wonderful examples of that Art Deco period. Also Grand Central Station, particularly the way one glass area lets the light in and the way that light falls, really quite beautiful, lots of marble, or at least that's how I remember it.
Penn Station for the hustle and bustle, we got an Amtrak train from there all the way down to Savannah. It's a hub to travel across that vast continent.
Seaport area for fish restaurants.
I think NY parks are somewhat underwhelming, Central and Battery were the ones we saw, compared to London's parks, my feelings were they were nothing to write home about. We did see the John Lennon memorial in Central Park when we had the kids with us. Last time we were there, I found I didn't really like the area around Times Square, just too much of a sensory overload and their subway is really dirty and quite horrible. I did like their SoHo, much better than London's that's for sure, nice shops and coffee houses, and the Tribeca district was also nice.
It's a great city, my very first impression when riding in from the airport, wow! it's like being in a forest of tall buildings, and it's somewhere where I think many of us feel we have been before we ever go there due to how filmic it has been over the years. Do the open top bus such a good way to see everything it has to offer, great for hopping off and on.
Have a great time it'll be a splendid experience.