I plan to start around Duluth/Superior, go eastward across the top into Canada, and back west along the southern coasts. The only thing I want to skip is the western Lake Michigan coast in Illinois 'cause I grew up in that area. I thought about traveling by mule train or recket sled, but I’ve settled on a car.
What should I see and do?
If you don’t mind things that are purposely touristy, Mackinac Island is a good place to chill out for a day or two.
Are there things to see, or is it more like a chill out on a beach thing?
You could go to the least visited National Park in the lower 48 - Isle Royale. There are day trips over to the island leaving from Grand Portage, MN near the Canadian border.
What time of year? Traverse City, Michigan in August has a cherry festival. I ate way too much cherry pie there one year. Plus Sleeping Bear Dunes is nice. Oh, and I took a ride in a glider just south of there. That was pretty cool.
If you haven’t already done so, get to Lake Superior Circle Tour. It has loads of information and facts. They put out a map that you might want to order, or you should be able to find it while in Duluth.
I have my Excel students load up the miles between cities and calculate the total, which is a surprising 1226 miles all the way around Lake Superior.
Don’t most of the areas around the Great Lakes have wineries? Ah yes, there is a “wine trail.”
Niagra Falls isn’t on the lake but you gotta go there. It’s right down the road 
In Cleveland, the Rock Hall is right on the lake. The lake comes in and laps the structure beneath the Hall. Gotta go to the Rock Hall.
Out west, in Sandusky, you got your Put-in-Bay, Kelley’s Island, etc. In Lake Erie, that is.
Right now it’s looking like late August or September.
I saw a bike tour map around all the lakes that totalled more than5 thousand miles, which was WAY longer than I imagined. OTOH, they extended the tour out along the St. Laurence, maybe all the way to Montreal, and probably added 2 or 3hundred miles just for that.
This sounds really interesting, assuming I can severly limit my wine sipping along the way. But dammit, I can’t find an actual map that that site that leads from one wonery to the next.
Huh, I just assumed by circumnavigation you meant by boat or canoe. Never occurred to me that you would drive. Perhaps to give yourself more of a challenge you could swim?
Or perhaps I can just kill myself now and save the pain of the heart attack later. 
Starting in Duluth:
See: The Lift Bridge (just cuz)
Eat: At Sara’s Table
Tour: Glensheen Mansion (ask about the murders now that they can talk about 'em)
Leaving Duluth-make sure to take the scenic route or else you’ll miss part of the lake. Pop in some Bob Dylan and enjoy the ride.
Next big town is Two Harbors and the appearance of Betty’s Pies. Grab a slice of pie (but ignore the rest of the menu.) This is the last major grocery store until Grand Marais too. The city also has a Pamida, and is the last of the kind of store until you get into Canada.
Leaving Two Harbors, there are 2 state parks that need a visitin’. Gooseberry (for the waterfalls) and Split Rock (for the lighthouse). Both of these have some great hiking trails too.
Next, take an Alpine Slide ride on Lutsen Mountain. Yes, even adults have fun doing this. Even if it is to take the chair lift in the summer to get great views of the area.
The rest of the drive is quite scenic and the next place to stop is Grand Marais, MN. This little town just feels right.:
Eat: Naniboujou Lodge for brunch and to see the Native American influence
Snack: World’s Best Donuts
Get a bumper sticker: Sven and Ole’s Pizza.
See: The lighthouse, the island around the lighthouse too
Do: North House Folk School. This place has amazing classes on how to build chairs or boats or knit et al. They also offer great sunset cruises. Check 'em out.
Before you leave Minnesota, pop into one last state park, Judge CR Magney. This is a gorgeous area to hike in. The topography is so atypical for Minnesota and will be the last of it for a while before entering into more of the plains area into Canada.
Grand Portage has shuttles out to Isle Royale (no cars allowed). It also has a fort which is worth exploring. Also, fill up on gas before leaving the country. It’s cheaper here. (It’s also worth noting since you’re coming from Madison that MN gas is cheaper than WI gas).
The next big city is Thunder Bay and while it’s cool to be in Canada, it’s just kind of…well, a shit hole. It’s not horrible, it’s just very working class and after the beauty of Minnesota’s North Shore, it’s kind of a let down.
See: The statute of the guy who was going to run all the way across Canada but only made it to Thunder Bay
Eat: Tim Horton’s (natch)
Hike: Sleeping Giant Park (There are some great views here).
I assure you, I was not drunk when I posted this – parhaps a small stroke?
Thunder Bay has the coolest name of all these places, so maybe I’ll satisfy myself with a picture of whatever sign is up at the city entrance. I hope they at least have a cool road sign.
Doesn’t sound like you’re going to get to the UP, but if I’m wrong, let me know. I can point you in the right direction.
Careful now, Terry Fox is a national hero.
“Only” making it to Thunder Bay means that he ran 5,373 kms on one leg.
…Not to mention the lung cancer, tendonitis, cysts on his stump, snow, sun, exhaustion, shin splints and an inflamed knee.
Back to the topic at hand:
Niagara-on-the-Lake is a must see, right across the river from a French fort from the 1700’s (Fort Niagara, now in the U.S.), and on the shore of Lake Ontario. Check out Forts Mississauga and George if you’re interested in the war of 1812.
I’ve seen you use the term “the UP” before. What does it mean?