I haven't done any November backpacking in Michigan so don't know for sure what would be best. Our summer favorites are Pictured Rocks, Isle Royale (which isn't an option now), and Porkies. From Chicago it's closest to the Porkies. For 3 nights, you could consider driving the first day and park in the lot near the Lake of the Clouds. From there you could do a short hike west to the first night's DRY camp along the escarpment - we didn't stay up there, but I scoped out the sites and decided that Big Carp 3 (BC-3) would be my top choice. Then the next day head down Big Carp and - depending on mileage preference - go Correction Line Trail to Little Carp trail heading toward Lake Superior (or for shorter, stay on Big Carp and go straight to Lake Superior). Lovely scenery and campsites along Little Carp. It will be MUDDY along the Lake Superior trail, so be prepared for that, but I think the gorgeous views would be worth it. Sunset will be further south now than when we were there, so if seeing sunset matters to you (it matters to me) try to pick a site where the shoreline hopefully won't block it. We did a
5-night trip and stayed 2 nights along Lake Superior, and I loved that. Depending on how much ground you want to cover, you could go further inland by Government Peak (which is a non-peak) but that was my least favorite part, at least in the buggy August when we were there.
If you decide to do
Pictured Rocks (which is gorgeous and I love!) you have to figure out a shuttle plan, as it's a straight trail from east to west (or west to east). I don't know how feasible it is to arrange at this time of year.
Whatever you end up doing, I hope you have a great trip!