My question would be, how long do you plan to spend in Michigan? I agree, going across the bridge from Mackinaw City to the U(pper) P(eninsula) is a great idea, and there are some great places to visit there: Soo Locks (Sault Ste Marie, which is pronounced "Soo Saint Marie), the shipwreck museum at Whitefish Point, Tahquamenon Falls, Pictured Rocks, etc.
As for getting there, don't follow the shoreline of Lake Huron until you get past the "thumb" (past Flint or so), or you will find yourself dealing with the traffic & other hassles of several big cities (Detroit, etc.) However, once you get about halfway up the lower peninsula, driving the shore route is fun - slower than the interstate, of course, but it's neat to look at the summer cottages, glimpses of the the beaches, lots of pine trees, etc.
BTW, the state park mentioned previously, located across the bridge from Mackinaw City, is Straits State Park. Some nice sites there; electric hookups available. Wilderness SP is also nearby, west of Mackinaw City, should you prefer this kind of camping to private CGs. Both nice, both popular; by now, sites may already be booked, especially for weekends.
Not sure how often the ferry runs but you can probably find a schedule if you google it. The island is worth a full-day visit at least.
