Exit the shuttle at Temple of Sinawava and head north along Riverside Trail. Paved, and wheelchair accessible, this 1-mile each-way trail follows the course of the Virgin River between towering 1500-ft high canyon walls. At the end of the paved trial, you can either dip your feet in the water and head back, or carry on into Zion National Park's most spectacular but easily accessible canyons, the Narrows, where the walls close in to as little as 25-ft in places. Trek into the canyon for a few hundred years or a few miles it's up to you.
If you go:
If you're heading into The Narrows, come equipped with a walking stick for balance and appropriate clothes/footwear; the river is the trail.
Links:

Floor of the Valley Road
Trailhead at Temple of Sinawava shuttle stop,
Springdale, Utah 84767 USA
Mailing address:
Zion National Park
Springdale, UT 84767 USA
Phone Numbers:
Park headquarters
+1 (435) 772-3256
+1 (435) 772-3256
Backcountry information
+1 (435) 772-0170
+1 (435) 772-0170
Message from RoadTrip America