I've been to New York twice now and both times my favourite thing to do was walk through Central Park. It is so beautiful and so familiar even if you're not from the US. You will always find something in the park that you recognise and it makes you feel like you're home in a strange city.
Also, Top of the Rock on a sunny day is breath taking. Rockefeller Center on it's own is something you definitely have to visit but head on up to the top for the most stunning city views you will ever experience.