I had picked the horseback ride on Zion, because I really had no idea what to do in Zion. But Bryce Canyon seemed more obvious. It was easier to find straight forward things to see, because the park website gives those "if you only have a few hours" option.
There are the 4 major view points: Sunrise, Sunset, Inspiration and Bryce viewpoints.
The Shuttle stops at all of those view points, but we can take a hike from Sunrise to Sunset (part of the Rim Trail hike).
The shuttle - unlike the Grand Canyon, and Zion - is not mandatory. So you can choose to use your own car. But they do prefer you use the shuttle. Here's the greatest advantage of the shuttle, you don't have to come back to where you left it. The thing that stinks about the shuttle is that - unlike the Grand Canyon - they don't tell you how long is the round trip.
Here is a list of the easy hikes (taken from the park's website):
Easy to Moderate Hikes
These hikes are classified as easy to moderate difficulties as they have
gentle grades and minimal elevations changes. They include:
Mossy Cave (.8 mi/1.3k round trip)
Streamside walk up to a mossy
overhang and small waterfall. (Waterfall flows May to October) - it looks very interesting, and it's only 1.5 Km, but the climb is 300 feet, vs the climb between sunrise and sunset - 34 feet. Also, if you only have a few hours, driving to the Mossy cave start point might be a little time consuming. Mossy Cave is all the way up on Route 12 and the shuttle route does not include that stop.
Rim Trail (0-11 mi/0-17.7 km round trip)
Outstanding views of hoodoos
from above. Trail is paved and fairly level between Sunset and Sunrise
Bristlecone Loop (1.0 mi/1.6 km round trip)
Hike through spruce-fir
forests to cliffs with bristlecone pines and expansive vistas.
Queens Garden (1.8 mi/2.9 km round trip)
This is the least difficult
trail into the canyon. Using your imagination you may even see Queen
Victoria at the end of a short spur trail.