congrats!
I wouldn't bother seeing anything in Newark. it's one of the armpits of the nation.
in NYC though, I would definitely check out the Museum of Natural History. it's really cool. and I wouldn't pass up the chance to check out Lady Liberty or ride the Staten Island Ferry (even though one crashed again recently). if you have time you should go to Central Park and try to count all of the statues there.
but you absolutely, positively, must go to John's on Bleecker Street and have the best pizza in the world.
oh yeah, no trip to NYC would be complete without a hot dog and a pretzel from a street vendor.