Helicopter rides into the Grand Canyon from Vegas are a lot of fun.
In New York the first thing you should do is go to the apple store and buy a laptop and 5 ipods like everyone else does.
Some of the comments below are good but some are tourist traps you can do without
A Statue of liberty in Summer = Hot nasty death trap - Think auschwits of America. You wait out in a long line in thew sun, get on an overcrowded boat go to liberty island for a lot longer than you need to be on a small island. There's a small museum, a gift shop and an overpriced cafeteria you can't go into the Statue most times now and if you can its a tiny staircase inside a huge hot tin can filled with hundreds of others on the same staircase. Enjoy the view from the Circle line instead.
Adam is right Hayden Planeterium is pretty cool.
Chinatown is for American tourists looking to buy cheap designer knockoffs or things that are generally cheap and will fall apart in a few days. With the sucky dollar you can buypass chinatown and go for the real goods in SOHO, Meatpacking district, or midtown 5th ave, madison in the 50's and 60's. If you want a great chinese meal though go to the Peking Duck House in Chinatown and get a duck it is out of this world.
Central park and the columbus center are nice.
If you post when your coming I can give you some better suggestions, for NYC.
Between NY, Vegas, and LA you'll probably use up two weeks, easily.