With the exception of state land...Unless you have permission to be on the land camping, it would be illegal to just head down a logging road and setup camp in the woods somewhere- especially if you are using some sort of motorized transportation to get you there. You can pretty much hike just about all the the bush (given it is private, but CFA, land. Get a plat book to help you with that) and I suppose you probably would not get run off or arrested if, on you hike, you pitched a tent and slept for the night. Quite a few folks do that. Do not take this as permission, it might even be legal under the rules of the CFA to pitch a tent if you are on foot only. Hunters can set up temporary blinds, so perhaps a tent falls under those rules. The DNR could fill you in on those rules.
A great place (not exactly in the Keweenaw) is the Porcupines Wilderness State Park. They have some camp sites and even a few cabins. Most are quite remote and you could stand the chance of being the only one there.
Quite a few campgrounds in the Keweenaw too, some are more crowded than others. Here is a link:
http://www.keweenaw.info/lodging/campgrounds/
-John