We just did that same trip, albeit in reverse order, going east to west.
Here's where we stayed, and what we saw:
At Munising: Bay Furnace USFS Campground. Beautiful campground about 2-3 miles west of Munising. Right on Lake Superior. Nice camping spots, some right on the shore. It isn't a parking lot situation like at the Munising Tourist Park campground. The sites have some space between them. No hookups, but if you will only be there a few days, not a problem. Historic Iron making furnace right next to the campground. Take the afternoon Pic Rocks boat tour, as the sun is in the western sky and lights up the colors on the rocks much better than during the morning, when they are in the shade.
At Manistique: Be sure to visit Kitchi-Ti-Kipi (Big Spring)at Palms Book State Park. Very Impressive, crystal clear spring where you can look down 40 feet and see trout swimming at the bottom and see the 10,000 gallons of water per minute bubbling up through the sand at the bottom. No camping at Palms Book, but Indian Lake State Park is nearby and has camping.
At Mackinac, we stayed at Straights State Park, which is right on Lake Huron and near the base of the big bridge. Electrical hookups available and great views of the bridge and island. Be sure to do the tour and lunch buffet of the Grand Hotel. You will feel like aristocracy!
Near Traverse City, we stayed at Interlochen State Park. There is MUCH to see in this area. Be sure to take a trip to Sleeping Bear Dunes and take a drive on the scenic byway. Very impressive.
We enjoyed all the campgrounds we stayed at and all the places we visited. OF course, these are just our suggestions. Have a great trip.