Shane, Googlemaps will break this down for you, but from Banff you are looking at roughly 3+ easy hours to Jasper. Assuming reasonable traffic. Then you turn west, four hours to Prince George, then four hours to Smithers and then four more hours to Prince Rupert. 15-16 hours of driving give or take.
At Pat and Steelhead suggested, the Icefields Parkway between Banff and Jasper is incredible, and that scenery continues for about the first hour past Jasper when you head west.
To break the drive up some, I would suggest the first night that you stay at or near Mt Robson, which is roughly that hour west of Jasper just so it is somewhere closer to halfway. Especially if you are camping. That way you get to look at one of the most magnificent mountains a person can (Mt Robson). That also gives you a few extra hours the first day for sight-seeing in what is absolutely the most beautiful part of the trip if you like large mountains.
If you are hoteling it, there should be a small hotel another few minutes west of Mt Robson at Tete Jaune Cache. It is on the Fraser River and is a beautiful location. If it is not open or you want a nicer hotel and more amenities, from Tete Jaune you can drive south a few minutes to Valemount which has nicer hotels. A handful of miles out of your way however.
From there, I would pretty much push through 7 hours to Smithers for the second night. From Mt Robson, the scenery is very nice until you get to McBride, but then the two hours from McBride to PG is ... not so stimulating?
Flattish land with trees and not much else.
PG will have the cheapest gas you will see in BC on your trip. Costco is there with their cheaper fuel, which forced the other gas stations to compete.
From PG, it's farm land through Vanderhoof and Burns Lake to Houston where that bear is in the window. Three hours plus a wee bit. Then you are getting back into the hills and the Bulkley Valley which is very pretty as well. 45 minutes from Houston to Smithers, where I suggest you stay the second night.
Then the last day you have an easy four hours to Prince Rupert, with Terrace about halfway.
One other thought. I will disagree slightly with Dwayne. You are never more than two hours between gas stations. Banff, Saskatchewan River Crossing, Jasper, McBride, Prince George, Vanderhoof, on and on. I wouldn't worry about taking Jerry cans. You will curse traffic on this trip more than you will worry about feeling isolated while looking at your gas gauge. The cheapest gas you will find is in Alberta and Prince George. I would fill up in Jasper and PG, then when you get to Smithers smile and bend over.
Smithers gas prices will likely be 50 cents a gallon more than PG and Jasper.