The Henry Vilas zoo is free, and a great place to spend the afternoon before the wedding if you came into town on Friday!
The arboretum is great escape from the city if you want to take a hike through the woods, prairie, or stroll through the gardens. Located a short way from UW Madison campus it has over 20 miles of hiking trails and 1200 acres of preserved nature inside of the Madison city limits.
The Dane Country Farmer's Market on the capital square is a must see. Grab a loaf of Stella's cheesy bread, a fresh baked pastry, or some fresh apples. Afterwards, take a stroll through the Wisconsin State Capital, down State Street, or head over to the Memorial Union Terrace for some coffee near the water!
The terrace is a wonderful place to sit and soak in the beauty of Madison. Right on the shore of Lake Mendota, you can watch sailboats going in and out of the docks. There is coffee, ice cream, and various food available for purchase.