There are no reservations, fees, or permits required for camping on Grand Island [1]. The island has two designated campgrounds at Murray Bay (two sites) and Trout Bay (four sites), offering the relative luxury of pit toilets and fire rings. Backcountry camping is permitted throughout the island as long as you stay off the tombolo, off private property, and at least 100 feet away from lakes, streams, cliffs, trails, roads, and natural research areas. No ground fires permitted. And remember, there is no drinking water anywhere on the island, so come prepared.
Links:
[1] http://www.moon.com/destinations/michigan/michigan-s-upper-peninsula/the-eastern-upper-peninsula/munising-area/grand-island-national-recreation-area