Angel's Landing is one of the most breathtaking hikes I have done. I think it is worth going to Zion NP, just for this hike. The first pic below is the view of Zion Canyon from the Angel's Landing summit. The ones after this are pics in order, from start to end of the hike.
The Trailhead for Angel's Landing is at "The Grotto" Shuttle stop, and very easy to get to.
You get off the shuttle, cross the zion scenic hwy and head north to approach a bridge...
Cross the bridge, turn right and head up the winding trail...
From that point on, there are no forks and the trail is pretty easy to navigate, all the way to the summit
At one point, you reach a series of switch backs that look like a set of walls, stacked up one upin the other...
Go past the switchbacks, hike a little more and you get up to "Scott's Lookout". This is a good turn around point for those with a serious fear of heights!
But, clearly, as you can see... not many seem to heed the warning signs :-)...
And then, you finally get rewarded with these spectacular views...