Spending a full week in NY would make you more pressed for time.... I live in Los Angeles and personally, this is my list of musts:
Grand Canyon for sure. If it helps, I had a little less than 24 hours to spend there when I went, but found for myself that that was plenty (I really only cared about seeing it though, you may want another day and book a mule ride). There's a shuttle that takes you from one end of the South Rim to the other and I was able to see most of that side in about 6 hours. Definitely catch a sunset there. And from the Grand Canyon you can go to Vegas (fantastic shopping, three Louis Vuitton stores,
Gucci, etc etc). Death Valley is about as fun as the name sounds, it personally wouldn't be on my list of must sees on a 2 week trip.
Yosemite (and everything Redney mentioned in her post, Sequoia, Tahoe, San Francisco, etc)
Yellowstone! OMG Don't miss Yellowstone. It's right up there next to the Grand Canyon I think.
If you want to see LA you really don't need more than a day, nothing fantastic here (of course, I live here, so my perception obviously comes from someone who sees the damn place day in and day out, but if you come, consider taking a tour of a studio. I suggest Warner Brothers, it'll be the best bang for your buck and give you a Hollywood experience, and you're pretty much guaranteed to see someone famous on that tour if that sorta thing tickles your fancy, perhaps even try and catch a taping of a TV show. PM me on that one for more info if you want).
The above, if you wanna take some time, could probably be pulled off easily in a week and a half depending on how you decide to travel (drive or fly?). You COULD do it in a week, but you'll end up feeling rushed I think.
I would almost make a circle... Perhaps start in Vegas, then go down to the Grand Canyon. From there come up to LA, then just head up the coast (however Kings Canyon/Sequoia is a little more inland, so for that you'll have to figure out how you want to route your trip, maybe skip Santa Barbara), and head all the way up to San Francisco, Yosemite, Tahoe. From up there you could catch a flight then to Yellowstone if you decide that's a stop you're interested in and from Yellowstone head to NY.