The wedding doesn't start until 4pm, so we highly recommend you take the time to visit the (very popular) Dane County Farmer's Market on the square. Get there early, as crowds can be impressive, and grab a great cup of coffee, some cheese samples, and a pastry or two. And don't hesitate to try Stella's Spicy Bread, it's a Madison tradition.
And while you're there, take the time to visit the historic capitol building (pictured above). It's open to the public and free tours are available.
Who doesn't love a good zoo? And a free one? Amazing. The Henry Vilas Zoo is definitely worth your time, even if all you want is a short stroll to see the polar bear or a quick glance at Maggie's peeps (she makes that joke every time she sees the flamingos as the zoo...).
There's an indoor aviary, herpetarium, and primate house, as well as a Children's Zoo (with a train and merry-go-round, which are not free, but also not that pricey).
Looking to experience a bit of the college life? Visiting the Madison Terrace is a highly recommended summer activity. Enjoy some Babcock ice cream, pub food, pizza, or a cup of Peet's coffee and then grab yourself a seat on the terrace looking over Lake Mendota. If you're in town early, free concerts or movies run most evenings.
PSA: You'll need a union membership, student ID, or alumni ID to buy alcohol on the terrace.
One of the most charming components of Madison is the easy access to nature. The UW Arboretum is a great place to talk a leisurely walk around Lake Wingra (you can also go to the other side of the lake and rent kayaks, paddle boards, etc.).
If you like to hike, you're an hour away from one of the best spots in Wisconsin. Devil's Lake is a stunning State Park outside of Baraboo (also a great spot to stop if you're into Circus history). Maggie recommends a stop at the (less popular) Palfry's Glen area of the park.
There's really no shortage of great things to do in Madison and the surrounding area. Olbrich Gardens, the Chazen Art Museum, Children's Museum, American Player's Theater, and the list goes on... visit the City of Madison website for more ideas and don't forget to do a little Google Search to see if there are any concerts or festivals going on. You're never far away from (usually free) live music in Madison during the summer.