This is one of my favorite activities in Madison. The Capitol city bike path is a paved bike only route that starts right downtown and winds around the southern boundries of Madison. The path is incredibly varied and you get to see the lakes, the downtown, the posh neighborhoods on the near west side, the arboretum and farm land all in one trip!
Start at Willy Street Bikes which is 3 blocks off the Capitol square on the corner of Williamson Street and John Nolan Drive. Then keep lake Monona on your left and start down the lakeshore bike path. After you pass the colliseum you take a right on the train tracks which is dirt for about 100 yards and you connect with the path and off you go. You stay on the path all for 15 miles or so untill you come upon Seminole Highway and take a right to go back into town. Later this summer you will be able to take the trail right back into town but they are currently working on that part. Maps are available at the bike shop.
The trail has few hills and I often see rabbits, deer, hawks, and snakes on the way. It is a wonderful way to see the city.