Glen N.
Yelp
One of the best hikes in the world. Seriously. I mean, it's not as narrow as the Narrows, and you won't see the flight of angels, nor is the trail misty, or are there any fractions of domes, but...
1) The family-friendly trail is super easy: less than half a mile, with a gradual 300' elevation gain.
2) The trail is pretty enough: a left at the fork takes you to Mossy Cave (actually a shelter cave or grotto, filled with moss or icicles depending on the season). A right lets you follow a shallow rock-bottomed "river", which is actually an irrigation ditch dug with picks by Mormons in 1890-1892. There's also a picturesque bridge for photo ops that is long enough to fit all their wives.
3) The trail has a payoff: a waterfall about 20 feet tall that empties into a small and shallow pool that is safe for monitored children. You can scramble the (slippery) dolomite limestone rock to go behind the waterfall. Or you enter the waterfall, though I stuck only my head and shoulders in and it felt like a pillow fight with the Baltimore Ravens.
You can also hike just a tad further up to the top of the waterfall, but there are no safety precautions to keep a kid from slipping over, so keep an eye on the kids that you do like.
The only issue is the parking. First, the small lot fills up quick. Second, though it's outside the Bryce Canyon National Park entrance, it's officially a park fee area, so you may need proof of admission or a park pass.