This time of year some areas / roads are closed either for the winter or during storms, flooding, & snow build up. Check out these two links for current park info. / closures and for dispersed camping in what they call the backcountry/wilderness areas:
Death Valley National Park (U.S. National Park Service) (nps.gov)
Wilderness/Backcountry Use Permits - Death Valley National Park (U.S. National Park Service) (nps.gov)
Be sure to read the rules & guidelines for backcountry camping and I would also recommend filling out & submitting the
free Backcountry/Wilderness Use Permit Application. I also give a copy to my emergency contact:
Backcountry Permit (nps.gov)
It's an enormous park and there are tons of places to "get away" & to get lost or stuck if you're not careful. Although there's no camping along the trail, I'd highly recommend driving the Titus Canyon Trail (if the weather permits). It's quite the experience and not very difficult at all. Again, depending on weather conditions and recent amounts of rain. Please double check, but I'm pretty sure you can disperse camp, or at least dry camp (designated campground with a table & fire pit) in the area around/between the Ubehebe Crater & Scotty's Castle (currently closed for repairs). If you drive Titus Canyon (It's a 1 way road) when you exit the canyon and reach the intersection of Scotty's Castle Road, turn right instead of left (back towards the paved road).
I'd recommend stopping by the Ranger Station at Stovepipe Wells to get the most current conditions, maps, and ideas of where to disperse camp.
Also, check out the RALLY POINT on this Forum titled "Spring Time in Death Valley" by PortageBay. He will be in the park @ Texas Springs Campground in Stovepipe Wells until mid-April. He's an Overlander & is offering to assist anyone who wants to disperse camp and/or off-road in the park. We'll be stopping in to see him this weekend for some help & advise.
Hope this helps...