The Frank Stella's are the best. They are all over the city and they always look amazing. Two of my favorites are the Saatchi and Saatchi lobby (pictured) and the Citi Corp building in Midtown.
The oldest still-operating restaurant in New York City, still in the family of the original founders. At Christmastime, it's decorated to the nines. Go with a big group: portions are large and the wine flows liberally. Look for the little buttons on the walls: in the old days, the mafia would hang out in the back room, and if diners saw the cops come in, they'd press the buttons so the mafia guys could run out the back.
You can't say you've seen NYC until you've seen it from a boat. Hop on the ferry from anywhere to anywhere and you'll see what I mean. Not only will you see excellent old buildings and factories--the inner workings of the old industrial city--but you'll head out under working bridges and see the skyscrapers in all their towering glory. And once you've done it, do it again, at night.