I wasn't able to stay here as it was full, but I did want to let others know of a good option nearby. 

There are two other campgrounds pretty close. One is called Sunset and is right across the road. It did not look very interesting, but you could walk from your site to the Death Valley Ranch, which has a saloon, restaurant and nice little oasis like setting for those looking for some shade and to grab things. 

I did stay at the Texas Springs Campground, which is just up the hill, about a 3 minute drive away. Was a bit more interesting with the setting amongst the hills, etc. with a bit of a view. It is a first-come-first-served, but seemed to have plenty of spots mid-day, mid-week, beginning of April, if the NPS is full. Also, great proximity to many sites in the National Park. Hope that helps!