A Wyoming Black Hills whitetail hunt is one of my favorites (second to elk archery hunting in September). I have been doing it for 25 years. Here are a couple of things I have learned while hunting heavily hunted public land.
Even though the season is the entire month of November, it is usually best to hunt the the 3rd or 4th week.
When I first started hunting there, I did a lot of still hunting in the thick forest. It was frustrating. I saw a lot of tails and got very few deer. Somewhere around the tenth year (I was slow to change the prairie hunting habits I grew up with), I decided to stand hunt. Since then, I have shot a buck every year.
Several years ago, the whitetail population in the Black Hills took a hit from a couple of bad winters and disease. It is now coming back. There should be a good crop of small to medium bucks. You will need to get lucky to get a real big one on public land this year.
Just a warning...once it gets in your blood, you will be going back year after year.
Good luck!