I did a short vacation there last year. Not camping, so I can't help with where to stay, but I can tell you some of the things I recommend.
We started in Whitehorse, drove a loop: drive to Skagway AK, ferry to Haines AK, drive to Haines Junction YT, drive to Whitehorse. Then drove to Dawson City and back to Whitehorse.
The road from Haines AK to Haines Junction YT was incredible. I grew up in B.C., so I've seen mountain roads before. This scenery just blew me away. Excellent quality road, btw. It climbs from sea level at Haines AK up to a high plateau. The plateau is incredible. Words won't do it justice. As you get close to Haines Junction YT, you start to drive along the edge of Kluane National Park. Again, fantastic mountain scenery. I wish we had had some time to explore the park.
If you do venture down to Skagway, I recommend the White Pass and Yukon tourist train. It is a day excursion that takes you out of Skagway up to the summit of the White Pass and back again.
Dawson City is a lot of fun if you're a history buff. The surrounding territory is very interesting with respect to the obvious changes that the gold mining have wrought. And from Dawson City there's a highway that heads west, called the "top of the world" highway, that has some incredible views.
We had a look at the Dempster Highway that heads north from near Dawson up past the arctic circle. There are lots of warnings about this road. From what little we saw, the warnings are warranted. I think I would take the road, but I'd definitely be careful and prepare for it.
One thing that struck us odd about the Yukon: it had excellent coffee where ever we went. We speculated that because they're so far off the beaten transport track that they have to have their own local roasting houses. But for whatever reason, very good coffee every where.
2013 Escape 19 ("The Dog House") , 2012 Nissan Frontier