Colorado Dale, thank you for the input. I think I'll start trying to explore the trails on the weekends and see where they go. (Well, after I get another bicycle, or get mine fixed as the freewheel/freehub exploded on me). All I have to go on is google maps at the moment and according to them Platte to Decatur to Weir Gulch through some other streets still following Weir Guch to 1st to Harlan to Byers to Belmar is around 18 miles.
Dragging the route to go through Crown Hill Park shows it to be 21 miles. As you mentioned, I need to get a bicycle touring map and get out there and travel parts of the trails. There's a REI store near the South Platte River trail in Denver, isn't there?