If you are just doing the coast, you will miss a lot. Doing Hwy 1 in the Big Sur area, and there are a few others, in your dually could be quite exciting, especially on the parts where two small cars passing is a challenge. The state is huge, and some parts are better visited at different times of the year, than others. I would go to a travel agency to get all the info you can. Go to
http://www.visitcalifornia.com/ , lots of info there, too. If you have a library nearby, see if they have a collection of Sunset magazines, as there is a wealth of info on things to see and do, mostly in California. Have fun.