If you don't feel like dropping 20 bucks a night or more for a spot to camp, this is a great alternative.  FR 568 is about a mile long and has a ton of all types of dispersed camping on both sides of the road, from little tent sites to pull-throughs for campervans and trailers.

Not a terrible road at all.  I drive a little, low-clearance hatchback and was able to make it all the way to the end of the road and back out while scoping out sites.  Go the whole length and see what your options are so you can pick the best one.