Yellowstone is an amazing place (both because of the landscape opportunities and the wildlife) and Grand Teton National Park is also great for both. If I were you, I would try and plan for two separate aspects of your trip, landscape and wildlife since there is an abundance of both at Yellowstone and Grand Teton NP. It would take too long to give you all of the specifics, but there are definitely areas in Yellowstone that are known more for wildlife sightings then others (some mentioned by others in this thread). In Grand Teton NP you may want to take the boat ride on Jenny’s Lake and the hike after (You can go for a short distance or very far - it’s up to you).
Also, as others have mentioned the national parks in August will be crowded. Also, every year even aside from major construction projects they often repave the roads in Yellowstone. Since almost all of the roads in Yellowstone are two lanes (one in each direction) when they repave they close one lane of travel and traffic then only has the other lane to travel. Therefore, you often have to wait 30-45 minutes for your turn to travel that one lane. It can be frustrating, but if you know ahead of time that it will happen it is less frustrating.
Moab is truly unique and is great for landscape shots. I am probably not telling you anything you don’t already know, but the U.S. Southwest desert in August can be extremely hot (like 40-49 degrees Celsius (104 -120 F) or hotter). If you have not experienced that kind of heat first-hand it is difficult to convey what that feels like and what it means when you are hiking. If you plan to hike I would strongly suggest you do so in the early morning (6:00 a.m. to 10:00 a.m) and later in the day (6:00 p.m. to 9:00 p.m). If you hike any distance from park facilities there will be many places where there is no water available. So, I would bring and carry lots and lots of water. A large hydration pack works well, but I would carry other water too.
You may also want to consider checking out the National Elk Refuge in Jackson, Wyoming, as well as the town of Jackson (a/k/a Jackson Hole) which has a lot to do and see. The following is from the Recreation.gov web site (
https://www.recreation.gov/camping/gateways/1532). “Driving directions to the National Elk Refuge which is located just northeast of the town of Jackson, Wyoming, and directly south of Grand Teton and Yellowstone National Parks are as follows: U.S. Highways 26/191 pass directly through Jackson and 6 miles of refuge lands. The visitor center is located on the north side of Jackson at 532 North Cache Street, and the Refuge administrative headquarters is located on Broadway Street, 1 mile east of the Jackson town square. Directions are as follows: Latitude - 43° 33' 10.4400" N / Longitude 110° 40' 41.5200" W.”
Whatever you do, I am sure you will have a great trip. There are so many amazing things to see and do in any and all of the places you are planning to visit.