What's the premiere place in Madison to go for a bike ride? You'll get some disagreement, but most people, serious cyclists or not, will say the bike path around Lake Monona.
The bike path is 13 miles long, and is paved, but is not offset from traffic the entire way around the lake. Quite a bit of the way is on bike lanes of relatively busy city streets. Do not ride on the sidewalks in the city of Monona, as periodically the police issue tickets in the areas where bicycles aren't allowed on the sidewalk.
The easiest place to rent a bike for the path is Machinery Row Bicycles on Williamson Street by the lake.
If you have time, stop by Monona Terrace for something to eat or drink and check out the view of the lake (and the path).
If you're out for a serious ride, note that the path can be quite crowded on weekends and top speeds can be dangerous, especially down by Monona Terrace.
The bike path also hosts the Lake Monona 20 kilometer run in May - http://www.lakemonona20k.com/ - which makes for a good tuneup run for the Madison Marathon at the end of the month.
For a GPS Track, visit Bikely - http://www.bikely.com/maps/bike-path/Monona-Lake-Loop149554