If you want a surprisingly pleasant hike in Madison, I recommend the segment of the Ice Age Trail that runs through the University Ridge golf course. You can park at the research center off Pleasant View and hike through to the west end of the course. I expected it to be a bland walk across a golf course, but it was great.
Or just walk in the Arboretum. The path that runs along the south side of Lake Wingra is great. The Arboretum trails are the kind one can do in a pair of old running shoes and blue jeans. No fancy hiking gear is needed (unless it's snowy or icy).