The two most popular trailheads are:
1. Kathleen Lake
2. A’äy Chù Trailhead on Kluane Lake
A larger version (PDF) with established trails is available via the Parks Canada web page. Here’s a screenshot:
Best established hikes are:
1. Kathleen Lake
– Cottonwood Trail
– King’s Throne
2. A’äy Chù Trailhead
– Slim’s River West (trip)
– Sheep Creek
– Bullion Plateau
I drove out to look at the Dän Zhu (Donjek Route) trailhead. It looked pretty harsh. (Trip report.) I’m not so sure I’m up for that.
Kluane National Park Hiking Guide by Vivien Lougheed.
Leave a comment if you have other best hikes in this Park.
besthike.com 
“I’m not sure I’m up for that?” Who are you and what have you done with Rick you impostor?
LOL
…or is Rick just getting soft in his old age?
The problem up there is marshy tundra. The walk in looked like it would take all day. AND that is a route, not a trail, … something like what we had in Tombstone. But wetter.