There have been some questions about other things to do in lower Manhattan when visiting the above sites, but I don't think any of the threads mentioned either of these so they may be of interest.
1. Fiterman Hall is a block above the Vesey Street side of the WTC site, across from the little park with the red Jeff Koons balloon sculpture. The exhibit is of pictures of the building of the new trade center. It's been running for awhile but they don't seem to have an end date for it.
2. There are tours of City Hall, which is at the Manhattan end of the Brooklyn Bridge. Even if you don't do the tour, City Hall Park is worth going through if it's on your way (I've mentioned the park before but don't think I've mentioned the building tour). It's especially nice in the summer when the fountains are going and the plantings are in bloom, and there's a changing art exhibit. And there are benches!
Here's a partial recap of things that have been mentioned previously that you can google or search on TA, including some places to take a break. Maybe others could add on whatever I've missed or new things that come up.
Woolworth Building tour (requires advance reservation)
St. Paul's Chapel
Smithsonian Museum of the American Indian (free! and a great building)
Bowling Green Park (bull + benches)
Museum of American Finance
Federal Hall (free)
Trinity Church (and the Duane Reade across the street, which has pictures of the old ticker-tape parades on the second floor overlooking Broadway)
South Street Seaport area (for meals and Pier 15 for views/rest/ice cream)
Stone Street (for lunch/dinner)
The Elevated Acre (for views and a break)
Federal Reserve Bank (requires advance reservation)
Louise Nevelson Plaza hardly ever gets mentioned (maybe never) but she is one of my favorite American artists and her giant sculptures on this little traffic island (intersection of William Street/Maiden Lane) are impressive.
For details on food/shopping/events, the Downtown Alliance site is a good resource:
Coming soon (check with us before your trip to make sure it's really happening):
A new Battery Park, a lot of which is fenced off for now.
Pier A, a cute little fireboat house on the edge of Battery Park which will have food places (spring 2014).
Brookfield Place, new shopping/food/events (partially open summer 2014 maybe).
The World Trade Center Museum (mid-May).