Abrams Falls, Great Smoky Mountains, TN
Barr Trail, Pikes Peak, CO
Bright Angel Trail, Grand Canyon, AZ
Buckskin Gulch, UT
Huckleberry Mountain, Apgar Range, MT
Kalalau Trail, Kauai, HI
The Maze, UT
Mist Trail, Half Dome, CA
Mt. Washington, NH
Muir Snowfield, Mt. Rainier, WA
Backpacker has links to each.
I’ve posted similar lists in the past. Be careful out there!
There’s never been a confirmed hiking fatality on the Kalalau Trail. The Na Pali coast has a bit of exposure, but it’s not that bad. I’d take kids.
besthike.com 
Right; the Kalalau Trail is on every “hazardous” list I’ve ever seen, yet it could be done naked and barefoot. And undoubtably has been. It’s main hazard is once out at the end, and eating wild Guava’s and drinking water straight out of cascades, one doesn’t want to leave.
Like most Rodale publications, this list is geared toward complete novices. The most hazardous trails are those going to the summits of mountains with bad weather (Mt Washington!) or tricky terrain (Angels Landing), or both (Longs Peak).
Statistics indicate Tuckermans on Mt Wash is by far the most dangerous trail in NA.
Just on detail about the Kalalau Trail : it is hikable bare foot, BUT as I hiked it a month ago, it was pretty hazardous because of the weather. It was very wet, so the trail was very slippery, with no real feature to hold on, and the trail not really horizontal, so I must admit I kind of freaked out there. It was between the 7 or 8 mile stone and the very end of the trail.
You could think I am not used to hike, but with a mountaineering background, I would not consider myself as an average hiker-ish tourist.
The beach and the valley is definitly worth the hike, though !