Dylan,
The best areas of the park for landscape shots are in the upper section to the north. The wonderland of rocks being one of the better places. This is the area where the majority of the campsites are located. All of the Joshua Trees are located in the northern section of the park and it is part of the Mojave Desert. The southern section is lower in elevation and is part of the Colorado Desert. It's accessed off of Pinto Basin Road. The Ocotillo plant thrives in this part of the park and not in the northern section. Both areas are beautiful, but very different in their ecosystems.
As for tips for a newbie; I suggest shoot with your 16-35 lens, camera in Av mode with an f-stop of at least f11 and ISO at 100. Start from there and experiment. Joshua Tree National Park is a beautiful park that changes with the light throughout the day, so what may not look too good at mid-day may be quite different at dusk.
One other thing, don't use a flash at night to photograph any animals. This is a national park rule apparently. I was stopped by a park ranger who gave me all kinds of grief for photographing a tarantula at night with flash. He detained me for over twenty minutes, but eventually chose not to cite me. Just letting you know.
