See the World Trade Center site. Even though much of the site is obstructed due to construction, the WTC site is still worth your while. Everything from the pictures of the Twin Towers to the list of names of all those killed on 9-11 is especially moving if you've never been to the site before.
Visit St. Paul's Chapel. Right across the street from the World Trade Center site, this chapel may not be as large as some of the larger churches/cathedrals in Manhattan, but it's still special. 9-11 memorials as well as other artifacts can be found at St. Paul's. You can even attend a service.
Walk through the Financial District. The highlight of this, of course, is Wall Street, specifically the New York Stock Exchange. The giant American Flag hanging outside of the NYSE is one of those “must have” photographs for anybody traveling to the city for the first time.
Take a walk around Battery Park. This is an excellent way to enjoy Lower Manhattan on a warm and sunny afternoon. There is a special 9-11 memorial in Battery Park as well as merchants and vendors. You can also get a great view of the Statue of Liberty from Battery Park or simply sit down on one of the many benches and enjoy the scenery around you.
Visit the South Street Seaport. The South Street Seaport has something for everybody. Great restaurants with outdoor seating and numerous shops await you at the South Street Seaport. This area of lower Manhattan is great if you're looking for a bite to eat, to do some shopping or simply go for a walk both inside and outside.
Walk across the Brooklyn Bridge. Taking this memorable trip is an excellent way to either begin or end your day. If you have the time, you could even make the return trip on foot. Remember to bring a camera if you plan to take this walk.