The Grand Canyon Parashant National Monument has some scenic landscapes. I returned to California by taking some of the remote back roads through the monument. I did this last year also.
I only encountered one other vehicle, and that guy stopped to ask me for directions! Even more odd ... I could give him directions (there aren't that many roads in GC Parashant NM). Here's a map showing the route that I took.
I saw interesting rock formations rising up from the scrub.
The roads were in good condition, so any car with 7 inches of clearance could have handled it.
On my next visit, I plan to drive some of the more rugged roads, such as Hobble Canyon, Jump Canyon, Hidden Canyon. That will be an adventure since I can't find anything about them through google. Here's a photo of the Grand Wash, with the Grand Wash Cliffs off in the distance.
For amateur geologists, the USGS has posted a detailed geologic map of the area on this site. (the 32.9MB gwmap.pdf link at the bottom of that page)