The University of Wisconsin Lakeshore Path (also known as the UW Lakeshore Path) runs along Lake Mendota in Madison near the University. The most used part of the trail connects the tip of Picnic Point to the UW Memorial Union and the Union Terrace. The round trip is about 4 miles. Most of the trail is on a wide crushed gravel surface, but there are also segments of paved trail with soft shoulders that are separated for bike and pedestrian traffic.
Parking is a real hassle near campus, so parking out near Picnic Point and running or walking to the Union Terrace is probably better than the other direction if you have a car. If you're finishing up at the Terrace, you can get ice cream from UW's on-campus dairy operations inside the Union, or a beer outside. Going the other direction, there isn't much in the way of facilities out by Picnic Point, but there is a "rustic toilet" near the tip.
Going out towards Picnic Point on the trail, look for the Indian burial mounds. The area that became Madison used to be covered with them, but many have been flattened or dug up for development and construction.
You can find running information for the area here: http://witrackclub.org/runs/lakeshore.html
You can bicycle on this path, but you have to slow down in the areas where the path isn't grade separated - they are gravel and you won't be able to go very fast anyway.