There's more than 1 way to get to LA ... I'd say it might be better to get off the interstate. Here's a couple alternative routes and stops.

South of Las Vegas get off on 160 and head toward Pahrumph. This connects the southern Las Vegas Valley with Route 95, eventually. It's a decent ride that will get you up in the mountains a bit. Near the Mountain Springs Summit you'll find a turnoff for the ghost town of Potosi. It's a ghost town, so don't expect that much to be there. It's also off a dirt road, so only hit the area if you're willing to leave the pavement. The road itself up and over the summit is worth getting off I-15.

In Pahrumph hit 127/372 and head back west. This will take you to the eastern edge of Death Valley and hook up with highway 127, which eventually runs back to I-15. The reasonj for this loop is the mountains. It's also a decent way to avoid some of the traffic, though you won't necessarily save time on a trip to LA.

At Barstow, head south on California 247 (also known as Barstow Road) for Lucerne Valley. This will take you into the Mojave Desert of western San Bernardino County. You can then cut back on California 18 through Apple Valley and hit the interstate. I'd suggest, though, that you take 18 south toward Big Bear Lake. You'll LOVE Big Bear Lake. You can also stop by Big Bear Choppers, where you can get a t-shirt and see some nice "build it yourself" bikes.

California 18 runs along with 38 and will take you on the Rim of the World Highway. It's a decent highway, though a bit more crowded than it was just a few years ago. This road will take you on some good twisties, but watch for the California Hi-Patrol, they usually are along this section pretty regularly.

 

2kids3pets,

These are ALL great suggestions. I think your main determining factor will be the weather and the elevations. Some of those places mentioned are what is called High Desert. I've been in Pahrump when it snowed. Rim of the world is above the snow and frost line too. No doubt that you are a hearty Canadian who can take that kind of weather and conditions a lot better than most. But I don't think you care to experience it while on vacation.

So check the local weather for those areas before heading out.

 

I've been to the Gun Store.
It's kind of like paying for a really hot prostitute - very exciting, costs a lot and you shoot your load way too fast.

(Not that I have any kind of firsthand experience with that sort of thing)