We stayed at Baraga State Park for a week. It's a very nice campground, nicely located at the base of the peninsula that protrudes into the very middle of Lake Superior and the Northern most point in Michigan (which has some interesting history too, and the beginning point of US 41).
The drive from Baraga to Fort Wilkins State Park is beautiful. If you can get a campsite at Fort Wilkins State Park, you won't be disappointed one bit.
Copper Harbor is a quaint little town with a light house you can see, historic sites, lots of maritime information.
While on that peninsula also take the Brockway Mountain Drive and enjoy the absolutely 360 degree view of Lake Superior, and Michigan. There's a very nice parking area there. The road is a bit narrow, some chuck holes, but very drivable, and the view is awesome!
We also stayed a week at Wilderness State Park, near Mackinaw City. There was lots to see and do and explore there too. Fort Michmillimachanic State Park is right at the Southern base of the Machanic bridge. There's nice beach area there, lots of public park area, and a great town.
Travel farther South on the lower peninsula near Harbor Springs (check Google) and there are all kinds of opportunities for kayaking. I understand Little and Grand Traverse Bay is simply awesome for kayaking. I have a friend who love to go there for kayaking and a couple people I (use) to work with who have second homes in that area.
I don't think there is a bad place to go to in Michigan for camping. After all, it's called "Pure Michigan" for a reason.