I am guessing you are living in Wisconsin now. If so, you will find that typical property taxs in the Black Hills are about 2/3 of what they typically are in Wisc. Of course property taxs will vary considerably for one locality to another.
Someone mentioned that homeowners insurance and auto insurance will be less in South Dakota. I would not take that statement for granted. Homeowners insurance can be quite expensive in the Black Hills because of the danger of forest fires and hail damage. Like anywhere else, your homeowners insurance will be higher as you get farther away from a fire hydrant. Your dog will roam more to. [just kidding]
How well you can live on a given amount of income depends on how you define "living well." The cost of living in small towns is generally less than in urban area's, but the main reason for that is that there are usually fewer services in the small town and there will be fewer things to spend money on in a small town. Your cost of living will have as much to do with how you live as it will have to do with where you live.
You are also assuming you will have some income from part time work. You probably will find the pay scales for unskilled labor are a bit lower in the Black Hills area than they are in many other places. If you have some education or training in some field, you should do as well in the Black Hills as anywhere else.
The only other item I can think of right now is that if you like snow you will probably want to be around Custer or Spearfish. If you like milder winters, head for Hot Springs or north to Rapid.