Hope you enjoy your trip!
Two campgrounds that I recommend are:
Straights State Park in St Ingace, MI, but only if you are able to get a lakeside campground. Can watch the freighters trade through the straights.
Wilderness State Park just outside of Mackinaw City is a wonderful place to camp. Away from the craziness that is Mackinaw City and a wonderful Michigan State Park experience.
To make a reservation try
http://www.midnrreservations.com/campgrounds/index.cfm
If it isn't in your plans be sure to take a ferry over to Mackinaw Island. If health/weather/time permits rent a tandem and take the 10 mile ride (on paved roads) around the Island.