WHAT ARE THE MUST SEES FOR NYC FOR MOM AND TWO FIFTEEN YEAR OLD BOYS?

First, turn off the cap lock -- there have been some kids sending nasty messages on the forum, and they use all caps. Yours is a serious message!
Now: I love to take people to the top of the World Trade center for the best view of the city. It all lays at your feet (well way, way beneath your feet) and if you're up there around rush hour, you'll find yourself looking down on the traffic copters. If it isn't too windy, you can even go outside on a special terrace viewing area, and see where one of the Wallendas (?) went from one tower to the other on a tightrope. The boys will love it.
There is a museum of Radio and TV which has special programs for teens -- they
might enjoy that. What about Radio City Music Hall? Grenwich Village is a fun place, they'll probably recognize many spots from movie scenes. There's a huge street market on Saturdays near St Marks (?) Eat lunch at a sidewalk cafe and people watch. Take them to Little Italy for dinner one night. You walk down the street and it is one restaurant after another, garlands stretched across the street, pretty neat. Let them pick which one.

Chinatown & Little Italy (one is right next to the other), Museum of Natural History - recently re-done dinosaurs & history of human development as well as many other exhibits, Metropolitan Museum of Art - Egyptian collection and Temple of Dendur, arms & armor, Empire State Bldg., United Nations would all be ingtersting for teens, in my opinion. This would be much too much to do in 1 day but several could be combined.

IF they are into music -- the Virgin Megastore and MTV Studio (across the street) in Times Square near the Jumbotron. Wouldn't be MY choice -- but my 17 year old HAD to go there!

Agree with several of the above suggestions. If you only have a short time in the city you may want to consider one of the bus tours which are pretty entertaining -- we did one that went all the way around Central Park so you got to see midtown and the theatre district, the upper west side, Harlem, the upper east side, and it then stopped for lunch in Little Italy/Chinatown and then headed downtown. It was a great way to see a lot of the sights and major neighborhoods, and you could get on and off wherever you wanted.
The NBC studio tour at Rockefeller Plaza is fun for teens. When I was there a few years back we got to watch a Saturday Night Live rehearsal and got to watch Elvis Costello rehearse his set which was very cool.
Also, if you haven't been to Ellis Island/Statue of Liberty I thought that was a lot of fun and very interesting (Ellis Island mainly -- the Statue of Liberty is really best seen from the ferry anyway).

If you want 15 year olds to have a good time in New York, go downtown!!! Just take a walk through the East Village around Tompkins Square Park and your eyes will open wide. They'll love the characters all over the place. Greenwich Village is very cool for that age and the hippest shops are on Broadway from West 8th Street (near NYU) downtown all the way to Canal. They'll have a ball just looking at the street scene. Forget the usual tourist attractions. They'll find them boring, I predict. A good play for teens is Footloose and that's always on the half price board.

Have a good time.

Paul