Something tells me you also probably don't want to see a Broadway show (though Book of Mormon is good for people who don't like the camp and kitsch of your typical Broadway dreck). There are great museums all over New York - the Metropolitan Museum of Art has everything from Egypt to modern (though most of the modern is at the Museum of Modern Art), the Museum of Natural History has all the animals, the astronomy and also pre-Colombian art of the Americas, there's the 9/11 Memorial and Museum, I think you can tour the stock exchange on weekdays and Trinity Church near Wall also has tours of the church and its adjacent old cemetery. You can also tour the UN if you enjoy lots of internationalist propaganda but it is interesting even if, like me, you find the UN to be useless. I've never done the bus tours but they have those too. There's the Empire State Building, Central Park, Times Square, the Statue of Liberty and Ellis Island (but tickets in advance if you want to go into the statue itself), Grand Central Terminal, the Library...I mean the list really goes on and on, and that's just Manhattan. Besides that, there are plenty of places you can sit outside and have a nice meal and a drink or ten. You can also see the Intrepid Museum on the West Side - there are plenty of airplanes and helicopters parked on the deck of the carrier, and it's next to the Circle Line which does water tours of Manhattan.