Besides the Grand Canyon, Bryce Canyon National Park is probably one of the major attractions of the states and without any doubt an absolute MUST for every tourist.

The common way to experience the canyon is to drive the rim road and stop at the viewpoints. You'll already get awesome views of the canyon, but the 'real' experience is to hike through the canyon and its bizzare formations.
There is a very good trailnet in the park. You can combine almost any trails to a nice roundtrip.
We hiked the combination Sunset Point - Navajo Loop Trail - Peekaboo Loop Trail - Bryce Point and back to Sunset Point via the Rim Trail. You might wanna start early in the morning, since during the day, most of the trails are heavily traveled by horseriders and the dung of the horses doesn't make the air smell better...