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.
The Brooklyn Flea is another treasure trove of odd finds, cool artifacts, and handmade goodness. If you're looking for inspiration or just something cool to hang on your wall, you can probably find something here. And if all that treasure hunting leaves you hungry, you are in luck--there's a delicious assortment of local food vendors and artisans there too.
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.