Originally posted by Ripsnort
Grand Canyon and Yellowstone. Everything else can wait for your second trip to the U.S. Do Yellowstone first, then Grand Canyon, and then drive to Las Vegas and you'll have a nice "sampling" of the US.
Caveat:
If Yellowstone, don't go there anywhere near the time of a U.S. summertime holiday (Memorial Day, 4th of July, Labor Day), or Canadian summertime Holiday (Canada Day July1st, Civic Holiday 1st week August) and best if done during the week (Monday thru Friday) to avoid the worst of the crowds that Yellowstone sees.
Also, don't limit yourself just to Yellowstone: there is a lot worth seeing beyond the boundaries of the park itself. Wind River Indian Reservation may be worth a visit, Grand Tetons definately worth a look.
If the Grand Canyon, stay in Vegas as "basecamp" and visit the Canyons from there.
Again, really depends on what kind of vacation you are looking for. Lists what interests you, and the suggestions you get should be more applicable.