Visit the capitol square, the center of Madison. There many great restaurants and bars.

The Wisconsin State Capitol is open to the public and well worth visiting.

There are nice walking paths along the lakes (which connects to a 20k loop all the way around). If it stays warm enough, you may also be able to rent small watercraft and paddle around.

Walk around UW-Madison campus.

Visit the free Henry Vilas Zoo (near Lake Wingra and the University Arboretum).

There are >6000 acres of parks within the city of Madison.

Rent a bike and explore the biking system.

Go see Devil's Lake State Park not far from the wedding venue

Attend a Packer's game at Lambeau (not so nearby)