Trona is controlled (loosely) by the Bureau of Land Management (meaning it was open during the shutdown), and the area is marked and open with only basic restroom facilities. The road in is not paved, so take a tough vehicle and have a contingency plan. The hiking trail is maybe an hour or so long if you do all of it, but you can see all of it from your car, if you don't feel like getting out. I also use the word "trail" in a loose sense - you can pretty much wander at will.
A close up of the ground. And a lizard.
Ridgecrest, CA is the nearest city, 20 minutes to the north and west. Ridgecrest is the city associated with the Naval Aviation Base at China Lake, so it is pretty large and has hotels and lots of variety in restaurants.