I have marked Door Trailhead on the map and across the Door trailhead you have Castle trailhead which great too. You have ample parking at Door Trailhead and you have three to four small hikes here in this lot which is great as you will be on the Badlands terrain.
Photo Spot Details
During our trip we stayed at Cedar pass campground and they also have cabins. Staying here is the best to wake up early and be at right spots at right time rather than driving all the way from Rapid City or something like that.
The first photo was taken at Door trailhead parking lot are and the trailhead called windows. This area filled with wild mountain goats and the hike has marked areas so be careful not to stray away as you’d be at the edge of some cliffs.
For photographing needs I would go with a lens to cover 35 to 150mm for most of the needs, Tripod would be helpful for early morning or night landscapes other than that you don’t need one. Below are some of the images I shot near the Door lot and Castle trail which is across the parking lot.
Cedar pass amphitheater has weekend Fri-Sun Night ranger program around 9AM summer nights. This program has few people bringing in telescopes for you to view distant planets which was one cool thing to do here.