A.C.
As corny as it sounds, I would take them up to Hollywood. I've done that with visitors of all ages and they all love it. Just seeing the Hollywood sign is exciting. Grauman's Chinese Theater is great fun. They offer tours that are interesting and seeing a movie in there is an experience. It is really beautiful and I don't think there is anything like it in NY.
http://www.manntheatres.com/chinese/
You can take a tour of the Star's homes, again pretty corny, but very LA. There is a tour bus location on the corner of Hollywood Blvd and Argyle right next to the Pantages Theater.
http://www.starlinetours.com/los-angeles-tour-1.asp
There is a Ripley's Believe it or Not Museum on Hollywood Blvd.
http://www.laavenue.com/hripleys.htm
You can actually get around easily on foot or take the metro line that runs along Hollywood Blvd. There are lots of parking lots by the Pantages Theater and there is a metro stop right across the street from the Pantages on Hollywood blvd. Take it down to the Kodak which is also fun to walk around. Make your way back to the Pantages and hit Grauman's and Ripley's. End up back at the Pantages and take your tour. You'll be ready to sit and ride at that point. It is a uniquely LA experience.
The Petersen Car museum is rather unique. I am not a big car aficionado, and actually thought I was being very polite when I went the first time and I had a blast. It is very close to the La Brea Tar Pits.
http://www.petersen.org/
You don't say where you live, but a short drive up the coast to Ventura or Santa Barbara
might be nice.
A great and unique to LA museum is the Fashion Institute that is bound to appeal to two young ladies.
http://fidm.edu/resources/museum+galleries/index.html
A hike in the canyons? Venice Beach even on an overcast day.
Have fun!