What vehicle are you driving?
Anza Borrego Desert State Park has many places with beautiful views and things to go see during the day. (guide books are available) They do not allow ground fires, so be ready for that. Plenty of day run type trails. If you want real excitement then plan you adventure for the first weekend in March and go see the TDS (Tierra del Sol) Desert Safari. More rigs of every make, model and some homegrown jalopies than you can imagine in one place. Lots of nice off-roading type people there too.
For other isolation without too many restrictions there's the Panamint Valley area. Chiraco(sp?) Summit off of I-10 where the Patton Museum is located.
Have you considered doing the Mojave Road? Takes a couple of days to see all the features. Not too demanding and definitely primitive camping. Get the guide book(s) for markers and good info on the history. Runs from the Colorado River all the way to Barstow. All dirt too.