The National September 11 Memorial is the memorial at the site where the twin towers of the World Trade Center collapsed after the September 11, 2001 terrorist attack. The Freedom Tower, the new building, stretches so high in the sky and is impressive. The museum is filled with audio recollections plus personal artifacts of those who died. The memorial is a large piazza filled with trees and two square pools (the North Pool and the South Pool) where the buildings once stood. The pools have waterfalls flowing over their sides to the bottom far down below. The feeling at the memorial is sad and stark, and there are many visitors. The names of the almost 3,000 victims are engraved on the edges of the pools, arranged so that co-workers names are placed beside each other. The hundreds of swamp white oak trees are beautiful and turn golden in the autumn. The Survivor Tree is a callery pear tree that was planted at the World Trade Center in the 1970s, survived the disaster, and was replanted at the memorial. At night, the waterfalls are lit up, making for a pretty sight. You need a reservation to visit, which can be obtained online. Once you arrive at your designated time and day, you wait in line and are checked by security. 

Nearby, two blocks east of the North Pool, St Paul's Chapel on the corner of Broadway and Fulton Street, for years after the attack had a wall full of thousands of mementos that loved ones left for the victims: notes, missing-person posters, origami cranes symbolizing peace, baseball caps, fireman's hats. The wall has since been cleared and its contents archived but an exhibit brings to memory the rescue workers who helped so many and who came to this chapel when it served as a 24 hour relief center in the days after the tragedy. St Paul's Chapel has had a long history. It was built in 1766 in the Georgian style, and George Washington came to offer thanks here after he was inaugurated president in 1789!
Also nearby is Trinity Church (two blocks east and three blocks south of the South Pool), which makes for a lovely view at the end of the long tunnel of buildings that make up Wall Street. It's interesting to walk around Wall Street, and also to see Zuccotti Park, at Liberty St and Church St (one block east of the South Pool), the park where the Occupy Wall Street protests were held. Younger kids won't find anything of interest in this area so skip it if you can't come without them. This part of the city is kind of dreary, with its cold narrow streets- if you only have a few days in NYC, also skip it. 
After your visit, hop on the A or C subway line at Fulton Street and travel to High Street in Brooklyn to check out the amazing views and have some pizza at Brooklyn Bridge Park!

Directions

The National September 11 Memorial and Museum is located on Liberty Street at Greenwich St, New York NY 10006. 
Open Sun-Thurs 9-8, Fri and Sat 9-9. Last entrance two hours before closing.
Admission is $26 for adults, $15 for children aged 7-12. You can buy tickets online. 

Click on map for interactive view