Been to Arches National Park, Black Canyon, Bryce Canyon, Canyonlands Park, Death valley, Alaska Glacier Bay National Park, Montana's Glacier National Park , Grand Canyon,Wyoming Grand Teton National Park, Mount Rainier National Park, Rocky Mountain National Park, Sequoia National Park, Yellowstone National Park, and Yosemite National Park.
Not on one visit but on four different occasions as the time is constrained on each visit due to work commitments and schooling. All these places have unique landscapes. If you love nature (not concrete), then the above are the important sights to see in the US.
PS: National Parks in Canada (Yoho, The Rockies, Jasper & Banff areas, Nova Scotia etc) are really stunning too.