As for optional things...there are a ton:
a) Brooklyn Bridge - you can actually walk across it
b) St Patrick's Cathedral - One of the oldest catholic churches and probably the most impressive architecture I've seen in the US
c) 5th Ave - home to all the high end shopping and some cool stores too (Tiffany, Cartier, Saks, Niketown, Trump Plaza, NBA store)
d) Rockefeller Center - the Today show records here, has the outdoor ice skating, and you can go to the top and look out over the city
e) Empire State Building - you can go to the top and look out over the city. Visibility is usually 25-50 miles.
f) Scores
g) Basketball at Madison Square Garden or the Meadowlands - both the Knicks and Nets have home games during your time in NY
h) Hopefully, the Dallas/Giants game if I can get tickets
i) Seinfeld places - the comedy club he performs at, the diner, and the soup nazi. Seinfeld took place on the Upper West Side (which is where I live), so there could be more
j) Riverside Park - another park close to my apartment that has a view of the Hudson River and New Jersey
k) Grand Central Station - we'll probably end up here anyway, since we'll be taking the subway everywhere
l) Madison Square Garden
m) Yankee Stadium (in the Bronx)
n) Shea Stadium (in Queens)
o) James Coney Island (in Brooklyn)
p) China Town - you can buy great quality "fake" purses here for female friends and family. I'm sure they things for guys too...shirts, wallets, ties.
q) The New York Public Library
r) Wall Street and the New York Stock Exchange - also close by is the federal building where George Washington was sworn in as the first president. Alexander Hamilton is buried at a church near Wall St also.
s) A broadway show - there are tons of great shows and we can get cheap tickets at a stand in Times Square. Claire Danes, Jennifer Garner, David Hyde Pierce are all performing in shows right now.