I have hunted elk in (elk unit 1). In the higher Black hills the whitetails start migrating in September, by the 1st of October most of the whitetails have left. I have never hunted deer or know the season dates there, but the earlier the better for that area. The deer unit is a lot bigger than (unit 1 elk) so I am guessing the foothills would get better later in the year but I think the foothills are mostly private.
Hunted region A for many years on a ranch. Started out with 300 whitetails in a field every night. Great hunting. After disease and Lions took the toll it was down to about 75 per night. I real drop. Numbers have been coming back as I hear. I have not hunted there in 6 years. I stop by and check out the area two times per year. I rarely see a mule deer. If you find the right area you will be seeing deer. (note: I only archery hunted in Sept.) As someone stated... patterns change as the fall progresses. I hunted the Aladdin/ Hulett area. Good luck.