The dirt roads in Joshua Tree can be driven with any passenger car. I used to go rock climbing there. It's pretty good for that but it has become to popular.

Azusa is pretty good on the weekends purely for the amusement factor. It's fun to watch people get stuck in the mud. I live about 15min down the freeway. Over the years they've made the area smaller and smaller. In addition we haven't gotten much rain so it makes the CA mud really pitiful.

Places to go? Dumont Dunes, Calico, Johnson Valley, Big Bear, Gorman area, Pismo. Hook up with a club. Not being from the area it'll be tough for you to find the good spots.