In early August after the beginning of total darkness the Milky Way will be visible overhead. Most of it will stretch NE-SW, crossing the whole sky. All this will change depending on the time of the night, of course. But it's impossible to miss, and it arches overhead - so as long as you can see the sky, you'll be fine.
Any place in the Death Valley proper will be okay. Since there are few artificial lights, the sky is very dark everywhere. Even close to popular spots like Stovepipe Wells or Furnace Creek you will be fine - just drive 15 minutes away from the lights and you'll be in complete darkness.
I would only consider more mundane concerns such as ease of access, comfort, and safety. From an astronomical perspective it's all the same, as long as the overall horizon is low enough for your shot. I suggest scouting out the area during the day. Where the valley floor is pretty low, the horizon rises quite high.
Even if you start out from Ridgecrest, driving towards the Valley, as soon as you're close to the industrial facility NE of the town (not too close - a little before it, or a little past it) the sky is already very dark. That's maybe a 20 minutes drive from the town. Just pull over, and look up.
Definitely bring binoculars. This is not the usual city sky. Even in a small instrument, like regular binoculars, it's full of stars. You'll find little clusters and other interesting formations everywhere. Just make sure your elbows are resting steadily on the car's roof, and slowly scan the sky with the binocs. It looks amazing.
EDIT: This is probably obvious, but bears emphasizing for anyone reading this who are not familiar with the area - bring water, lots of it, and make sure your car's AC is working properly. You don't want to be stuck somewhere, without water, in 125 F / 51 C weather.