You can fit in a lot in two days.
If you want to do the traditional things then:
Empire State Building and have a beer when you get down at Heartlands which is a microbrewery
Staten Island - rather than pay to go to Ellis Island and round Staten, jump on the free local ferry
Walk in Central Park
Go and see a musical on Broadway
Other things that I like to do, but would depend on your time and whether you are interested would be:
Metropolitan Museum of Modern Art
Helicopter ride over the city
Walk over the Brooklyn Bridge
Walking tour of New York
I like just walking round New York. Its an amazing city and each time I go, I find museums and neighbourhoods that are great. Recently, I walked from the Empire State Building down to the Staten Island Ferry, taking in as much as I could, including the Tennament Museum which I found totally fascinating - and its located fairly close to the famous Katz Deli/Diner which is a must for lunch.
Last time I got a travel pass which allowed for use of the bus and metro and I found that invaluable.
And of course, there is always shopping! over 8 years ago