I am going to vouch for one very specific part of Michigan here: Isle Royale.

This isn't so much for just visiting but it is for camping/hiking.

For those of you unfamiliar with Isle Royale, it is the largest island on Lake Superior located in sort of the Northwest quadrant of the lake. Once upon a time people tried to mine on it but since the 1940s it has been a national park. Since it is located in the middle of Lake Superior it never really gets overflowed with people visiting the island so you can very easily hike into the island and disappear into the wilderness. At the same time it isn't completely barren and if you stay near the shore there are even small shelters you can stay in.

It also holds one of my favorite distinctions (from wikipedia):

Siskiwit Lake is the largest lake on the island. It has cold, clear water which is relatively low in nutrients. Siskiwit Lake contains several islands, including Ryan Island, the largest, which contains Moose Flats, a seasonal pond, which contains Moose Boulder. When Moose Flats is a pond, Moose Boulder becomes the largest island in the largest lake on the largest island in the largest lake on the largest island in the largest lake in the world