Dear Kit Inquiry
First off thank you for the question @mempasis. Joshua Tree is incredible place, it's kind of like Dr. Seuss and the Sahara had a love child, regardless of your kit or what part the park you visit it's going to be an incredible experience.
Lets talk about your kit. I believe the 24-70 and 70-200 will be an amazing kit for your first and single day trip to Joshua Tree. You will be surprised how much you can do with this combination. For me the most important thing about shooting landscapes in Joshua Tree is letting your feet do the work. You may not find the perfect shot at every pull out or car stop but if you give your feet space to roam, I promise you will find some inviting perspectives (I'll mention later where to go) Go off trail, if you see an interesting rock formation, hike to it. Don't be content with the beaten path or where the crowds are flocking. My best and favorite memories in Joshua Tree were when I scrambled up and over different formations and found unique spaces.
In terms of shooting with the 24-70, if you find yourself in a situation where you don't have a wide enough angle, change your perspective. Lay on the ground and see how a Joshua Tree arches above you, move back or forward, don't rely on the telephoto component of your lens, let your body and your vertical perspective dictate your compositions. If you see bigger rocks don't be afraid to put on the 70-200 and go exploring, I've seen big born sheep in the park several times and have always been close enough with the 70-200. Also, don't be afraid to get the 70-200 on and shoot some telephoto landscapes, you will be surprised. More important than anything else, get a feeling for the space and relate what you feel back to us through your photography.
The northern half of the park has much better topography and can be more visually stimulating. All of the Joshua Trees are on the northern half of the park as well as the majority of interesting rock formations. The Mojave Desert ecozone on the northern side is higher elevation and more populated with plant and animals. The southern ecozone, Colorado Desert is defined by more expansive deserts. Here is an NPS link with some good information https://www.nps.gov/jotr/index.htm.
I would begin by visiting the visitor center and the park entrance. Get a map and whatever else is necessary to plan your time. Before you get into the park pack all of the food and water you will need for the entire day, the last thing you will want to do is waste time on returning for supplies. Jumbo Rocks and and Hidden Valley really stand out to me every time I visit. They are really great jumping off points to get away from the car and really get a feeling for what the park is like. Do a little research, find 1 or 2 off trail areas you really want to explore and then share that time with road side stops such as skull rock and cholla garden. With your limited amount of time, the furthest south I would recommend going would be the cholla garden.
I hope this helps, if you have any followup questions. Don't hesitate to ask, Have an amazing time and let me know how it goes.
If anyone else has travel enquiries of their own please ask away :)