Before the wedding, enjoy breakfast on the state Capitol square at the largest, most diverse farmers' market in the Midwest (only open on Saturdays). There are so many vendors that you can get full on free samples! Yes, buy the hot spicy cheese bread from Stella's!
Take a free tour of the State Capitol, or just walk around and inside for free. Did you know that no building in Madison is allowed to be taller the state Capitol? It is built on the highest point on the isthmus in Madison.
Supper clubs really only exist in Wisconsin. What makes a restaurant a supper club? They offer brandy old fashioned sweet cocktails, have a relish tray or salad bar, offer delicious ice cream cocktails for dessert, and they only serve supper. Look for these details when you try to find an authentic one to visit. I trust this website's list of supper clubs.
Visit the funky artisan shops, art galleries, and restaurant and bars on this pedestrian-only (and buses) street that spans from the state Capitol to the university.