Oh there are so many things to do and see in New York City. You could spend several weeks and never be bored. When my younger son moved to Brooklyn, NY it was a good/bad thing. Living in California you never want your baby that far away, but for the good I love New York and now have an excuse to go often.
In January 2012 my son, his fiancé (reason for moving to Brooklyn) and I went to the World Trade Center Memorial. It is will worth the visit. The tickets are free, but you do need to get them in advance. (http://www.911memorial.org) You will be in awe of the vastness of the water features and the area. There are two identical water features that are an acre each – an acre! Around each are the names of everyone who lost their life that day.
There is a set of computers where you can look up the victims. It typically has a picture, a brief history and where their name is located on the memorial. You can print out a little ticket that will give you the location and then you can go find them. The person we looked up was Timothy J. Maude. (see picture) It helped give us a personal connection with the memorial.
We higher recommend going to the memorial. It is an important moment in our countries history.