On your way up:
Alaska Hwy north, Cassiar south
Once in Alberta take Hwy 3 west to the Jct with Hwy 22 take that north all the way to Hwy 1, then head west to Banff
Banff continue on Hwy 1 to Lake Louise then take Hwy 93 ( ice Field Parkway) to Jasper.
After Jasper take Hwy 16 east towards Hinton Alberta, just east of Hinton there is a Hwy Jct with Hwy 40 to Grande Cashe, take that all the way to Grande Prairie then head west on Hwy 43, once you enter BC will become Hwy 2 to the short distance to Dawson Creek
Once at Dawson Creek follow The " Alaska Hwy" ( hwy 97 in BC & Hwy 1 in Yukon) all the way north.
One the way back take Hwy 37 ( the Cassiar Hwy) south to Hwy 16, after that where every you want to go.
The reason I say go up the Alaska and down the Cassiar is you may hit the salmon spawning run on Fish Creek at Hyder Alaska which is 2km west of Stewart BC. Take the Hwy 37- A at Mazeaiden Lake / Jct ( Hwy 37 / Hwy 37-A) to Stewart.
If you head up in late June early July you may be to early. They are usually there about mid July until mid September.
My DW was raised in Stewart and I can tell you it is something to see.
Soup.