The Kickapoo river isn’t north country paddling, but it’s a great multi day paddle fairly close to Chicago. There are several outfitters based out of Ontario, Wi that do rentals and shuttles.
There isn’t anything quite like the BWCAW in Wisconsin, but there are great multi-day river trips. The closest thing to the BWCAW is the Sylvania Wilderness on the border of Wisco and the UP. It’s small (30k acres maybe), but you can portage and paddle some beautiful lakes.
St. Croix, Black, Wisconsin, nemekagon, Wolf, and bois brûle are great Wisco rivers to do multi-day paddling trips on. St croix, Black, Wisconsin, and namekegon would be the two I’d recommend for beginner level canoeists.
You’ve got some nice reservoir paddling with campsites on the flambeau and willow river flowages.
“Paddling Wisconsin” is a good source for trip info:
https://www.amazon.com/Paddling-Wisconsin-Guide-States-Routes/dp/0762738286