Copper Harbor has a gem with the Gas Light General Store. We often visit Copper Harbor and end up stopping at the Gas Light for something or other. Even though it is a small store, they have always had what we needed. Now, if you are looking for a very specific brand of something, you might not be as lucky.
The prices tend to be a little higher than a national chain grocery store, but that is to be expected given its remote location. It makes that up with the small town feel, friendly faces and surprise visitors. One time we went in there and a patron had a parrot on his shoulder. You'd never see that in a national chain store!