Wow, that's a tall order. But, there's two main opportunities. One is the Burke-Gilman Trail, which starts more or less in Ballard (that's the Northwest end), where you could start by visiting the locks. It doesn't officially start in Ballard, and it's a tough connection, but nice to see the locks. BG goes all the way over to Woodinville.
http://www.seattle.gov/transportatio...ntrailmaps.htm
The other option is the southern end of Seattle, the Interurban/Green River Trails. The ride along the Green River portion is pleasant enough, but I think you would probably do better on the BG.
Plus, you could try for a meet and greet with quite a few BF members doing the BG

. The RedHook brewery is a popular place to stop...
East Hill