If you can, try to stay one night on the island in a hotel or B&B. After the hoards of tourists leave, it is a lovely place. And a large part of the island is state park, but you can certainly ride a bike or hike anywhere in the state park. And rent a couple of bikes and ride around the island on the 8 mile long state highway that does not allow cars. You can even rent a "self-drive" horse and buggy to drive around the island. The horses pretty much know where to go and are pretty used to newby drivers! (If my adult son can drive one, anyone can, since he has never even been close to a horse as an adult.)
If you don't want to do those things, at least take a horse-drawn taxi around the island or one of the tours.
And the island is called "Mackinac" because it was settled by the French. The town south of the bridge is called "Mackinaw" because it was named by the British, but both places are pronounced the same. (Actually, the Indians named this place "Michilimackinac" or "Great Turtle." https://en.wikipedia.org/wiki/Mackinac_Island
Also, not too far from the northern end of the bridge is Sault Ste. Marie, Michigan, and the locks where the big freighters go through from Lake Superior to Lake Michigan. (They are the Soo locks, by the way, and "Sault" is also pronounced like "Soo" because it also was named by the French.) There is a city-owned campground about a mile east of town called "Aune-Osborn." It is pretty basic with water and electric and a dump station, but you can get a spot right on the river just east of the locks and wave at the deckhands on the ships as they enter the narrow St. Mary's Channel. If you are lucky, you will get to see two of the bigger ships pass each other in front of you. https://www.saultcity.com/aune-osborn-campground
And remember that the Edmund Fitzgerald sunk off Whitefish Point, so a 75 mile drive west will get you to the Whitefish Point Lighthouse and Museum. There is also the Tahquamenon Falls and Hemingway's Big Two-Hearted River, if you have more time. And don't forget to buy some fudge on the island and some pasties on the Upper Peninsula.