others have already covered most of what I'd have to offer.
Going to the north rim of the grand canyon from california pretty much ensures you're going through the northwestern corner of arizona, then into st. george utah to turn south, unless you've got some cross country expedition through BLM land planned (and if so, take pics and post the route).
Because of this, you're within an hour drive of Zion National Park, and it would be a shame to miss it. If you don't want to camp around a bunch of people, there is dispersed camping available in the northwest corner of the park, as well as a primitive campground with six sites. The hike up the narrows (ask a ranger) is amazing, and there is a place in town just outside the south entrance that rents "wet suit" socks with shoes that will make the hike up the narrows a lot more pleasant. A walking stick is also quite handy, since you're walking almost knee high through a flowing river for the bulk of the hike. The weeping rock is also worth seeing, and is an easy hike with no special equipment required.
About ten miles south of the airport in Hurricane, UT is an old mormon escape trail. Pretty easy drive, with the exception of one gnarly loose rocky off camber spot. Gorgeous views, and it's kinda sorta on the way into arizona from Hurricane to get to the Grand Canyon. If this interests you, I'll have to dig up the details and waypoints and such if this interests you.
On the way to the north rim, there is a fire lookout that someone mentioned in Kaibab National Forest that you'll drive by. It is usually locked, but the view from just below the locked cabin is amazing. There are also a few dirt roads that you can drive around in the national forest, some with views that rival what you'd find in the national park. Unfortunately, a good chunk of the forest burned in a fire last year, and there's a lot of logging going on in the area, though I don't think it's quite a clearcut operation that would require letting the oil out of bulldozers or anything. There is a ranger station in Jacob's Lake (where you turn off 89 to head to the north rim) that can provide information about that area if you're interested. There's also a dirt road that completely bypasses jacob's lake, possibly even Kanab if I remember right, heading straight to the fields just north of the north rim boundary.
When you get into the north rim, if you're driving a reasonably equipped 4x4, you should head out to sublime point. Ask a ranger if you can't find it on the map. It is gorgeous out there, and there are a couple of spots that would make good campsites if you want to be in the middle of nowhere with amazing view. Do remember you're in a national park, and tread lightly on the way out there though.
The four wheeling isn't anything ridiculous, then again, we were in a triple locked 80 with 33s and a 3" OME lift, so maybe it was a little worse than I remembered.
I have some pictures of the area somewhere. If you're interested, I can dig them up.