Get the nice folding "Bikeway Map" from Madison County Transit.

Another nice map is the "Riverfront Trail Map" from Great River Greenway or Trailnet, Inc.

Both of these maps contain some of the route Jerry STL is describing. Just be sure to check for trail closings.

The bike shop on Delmar has both maps and a few more. Free.

Here is the MCT Trails Map Online:

http://www.mcttrails.org/map.aspx

If you scroll in enough you can see the Riverfront Trail on the Missouri side.