There are far more things to see and far too much to talk about. I cannot recommend enough that you go and try it even just once. I believe that New York offers something for everyone and no two people will come back with exactly the same feelings about it.
When I think back to my reasons for coming to the USA for the first time, it was primarily for the universities. I had this grand dream that I could graduate in the UK and then go on to do a PhD Stateside, but now travel is what dominates my dreams practically on a daily basis and let’s face it travel is a far more practical (and certainly cheaper!) option. But when I was dreaming of USA study, I thought it would be good to go and see some of the best universities not only in the USA but also the World. So I choose to fly into Boston to see Harvard, MIT and then I could pop over to Brown in Providence and Yale in New Haven before going down to New York for NYU and Columbia so that’s just what I did.