For sure. There's routing and there's destination. Dempster is your best bet.
For rest of YK I'll add some comment that Milepost prob covers, IDK, have never used it :
When you come out of Robert Campbell Hwy, if looking to stretch your legs, there's a short hike at Five Fingers.
Keno is a bit of a drive in but has a few old buildings, small museum and a restaurant. The main attraction tho is prob driving up Keno Hill. Can walk around up there (should have some colour ?) or drive further and hike Hinton
We haven't hiked any Kluane. Leaving Haines Jct, keep an eye on the view behind. The mtn vistsa can be quite dramatic.
Can resupply and walk around Whitehorse, "downtown" and along the river. There's also Miles Canyon futher east.
If the weather is good, it's worth a side trip along the road towards Skagway. It's goes thru some pretty cool terrain. Don't have to go as far as the border. This side trip route could take you past Carcross desert. Again, walk around, on the sands.
Another possible side trip is to Atlin. The rd in is paved now so, not as much fun, but the town setting is beautiful. Can camp on the beach (Norseman CG) or further on there's a park. Also a hike up or part way, Monarch for views. Bit more of a drive tho.
Cassiar. The hwy is a long drive. Cross fingers the weather allows for views.
Boya PP can be great if it's not too busy.
The road into Telegraph is kinda cool. Unfortunately the neat, historic, old townsite was burnt recently and IDK what's left. It's hard to see much of the canyon from the road but there are some neat rock features visible.
Stewart was mentioned ... note crossing into Canada if you are carrying bear spray, it's "bear spray" not pepper or mace. And have it handy to show.
There's a number of Indigenous cultural attractions near Hazelton. OK campground beside 'Kasan. Stop at Moricetown to view dip netting and maybe purchase salmon.
Referring back to Alaskan Hwy,Tetsa (Toad R) was mentioned. About 10km west there's a worthwhile pull out to view Folding Mtn.
Further on there are some cool debris flow, gravel fans around Muncho. This whole area, from Summit Pass/Lake to Liard HS is part of the Northern Rockies and is one of the best stretches. Soak it in.
Summit lake in Stone Mtn PP has camping and some rocky hiking.