First off, let's point out a few obvious things:
1) You live in a ****ty location for roadtrips.
2) There is this little infamous place near you called BANFF where all these North American traitors got together a few years back to start us on the road to European Union like tyranny. I think that place suffices for the whole mountain experience and mimmicks the states directly below you guys well. If you guys want that, save the driving. I know the temptation to want to scoot out a bit and be in other states and countries always seems like it's more adventurous and enticing, but as somebody that has driven different places and then realized that those places weren't any better than the stuff we have in Utah, I might look somewhere closer if I were you so you guys can actually relax on your vacation instead of be in a car for half of it.
3) I think Vegas/Southern Utah would be a nice change up for Igloo dwelling Albertian if you guys had more time. Not worth only have a few days there though.
4) Utah cities are better to live in than to visit.
In summary, the Dakotas/Minneapolis would be a good blend of outdoorsy/urban, be a shorter drive than the Vegas scenario, and could be easily knocked out and feel like you got a good taste within a few days; go somewhere in Canada that's closer to you and relax, or go spend more time in Vancouver/Seattle/Portland since it will save you hours and would probably fit well into your timeframe.
Although, if you guys just really love being in cars.... stretching a trip to one of Chicago/San Fransisco/Vegas could still probably be pulled off and somewhat enjoyable if you drove fast enough, and are all worth visiting, assuming you guys don't turn into evil Jinns on the way like 90% of the people I know would in a long road trip scenario.