What does "off the beaten path" mean to you? I assume that means leaving the main ALCAN?
Its a long drive- how much time are you allotting to it? plan on spending time in Fairbanks?
There are a number of options- If you are going up the main route through Dawson Creek, BC to Fairbanks it is very straight forward and at no time any real risks. lots of traffic. Be sure to stop at Liard Hot springs, very nice. If you drive back down to L48 then take the Cassiar route down on the way back. can detour to Hyder AK.
At some point the detours through Glacier, Banff and Jasper national Parks are neat, but can have a lot of tourist. The Kootenay region (Fernie, Cranbrook) is less crowded and off the beaten path if you cross the border that way.
Further north a real detour would be to hit the Dempster Hwy! Very few ever do that drive.
If you want to see NWT take the North Canol road out of Ross River to mile post 222- thats where all the big NWT outfits drive to then chopper in. That is one long dirt road.
A more modest but worth while loop would be to go North at Whitehorse and visit Dawson City, Yukon. Then cross the ferry to the Top of the World Hwy into Alaska, through Chicken and catch the Alcan back near Tok.
So many options you can take