I've been to the Grand Canyon and Yosemite. Both are great destinations.
The Grand Canyon has to be experienced as words just can't do it justice. Its sheer size is enough to mess with your mind. It is truly breath-taking.
The giant redwoods of Yosemite will also stretch your mind. Standing the the base of one looking up it seems that it arcs almost behind you. Not only are the trees awesome, but the entire park has so much to see... Bridalveil Falls, Seven Sisters, Glacier Point (it had 28' of snow in July when we were there).
The US is such a large and varied country that there is no way to see it all, or even just hit the highlights. Figure out what kind of a trip you want and then find things that fit that. If you want cities, hit New York, Chicago, DC, LA, Boston. If you want tourist attractions, hit DisneyWorld/Land, Universal Studios, Sea Land. If you want nature, hit the national parks (we're covered up with them).