While I agree with your Brooklyn Heights recs, one could easily spend an entire day in the Heights surveying its historic architecture. But I agree that a visit to the Promenade and walking the bridge back to Manhattan are musts for every visitor to the city.
And although certainly no secret, I wonder how many tourists really take advantage of Central Park. When I was a kid, Central Park was thought to be a scary place for tourists. (Movies like Death Wish didn't help!) But it truly is a magnificent place that has lots to offer and that shouldn't be missed.