The hike up West Rim Trail to Scout Lookout and on to Angels Landing provides some of the best views of Zion Canyon. The climb to Scout Lookout and its fine view over Zion Canyon is paved and well graded. Just before Scout Lookout are Walter's Wiggles, a series of 21 tight switchbacks...At Scout's Landing, the trail ventures out a narrow peninsula with sheer drops of over 2,000 feet. It ends at Angels Landing and extraordinary views of Zion Canyon. Along this portion of the trail, chains have been afixed to help you navigate the more dnagerous, narrow passages. Do not try this trail if you have a serious fear of heights... West Rim Trail starts at the footbridge over the Virgin River across from the Grotto Picnic Area.
This is absolutely the best map available for hiking Zion National Park. It lays out the whole park three-dimensionally and shows more than 40 trails. You'll easily be able to see how to reach the trailhead and where the trail runs.
During the main season, you'll need to take the shuttle. Off season: From the visitor's center at the south entrance to Zion National Park, proceed north along the main scenic drive until the Grotto Picnic Area. A small parking area is on the left. The trail begins across the footbridge over the Virgin River.