Nothing fits that bill more than the Angel's Landing hike which takes you 1500 ft (450m) above the canyon floor to the edge of vertical cliffs overlooking the canyon. The hike in itself is about 2.5 miles (4km) each way, but the last half mile is the most challenging as it is not only very steep, ascending almost 500 ft in that last half mile, but the trail is along the narrow razorback ridge that runs out to the spot called Angel's Landing. The point was named Angel's Landing, by the way, by Frederick Fisher who was said to exclaim while exploring Zion in 1916 that only an angel could land on the monolith.
Looking at the accompanying photo of Angel's Landing you don't get the impression that what you're looking at is a narrow fin of rock, but that is in fact what it is.
Our reading about the hike online scared us, not just because of the steep climb (our average age qualifying for being "of a certain age", and we all have sedentary jobs), but also because we were weren't sure how we'd do on those vertical edges. But we were up to at least giving it a shot and going as far as we comfortably could, and hopefully all the way.
Anyhow, you can read the story of the hike and whether I made to Angel's Landing or not along with the photos I've posted. You can also see some shots I took along the Zion Canyon Overlook trail that we hiked in the late afternoon.
Angel's Landing and Zion Canyon Overlook Gallery
Angel's Landing and Zion Canyon Overlook Slideshow