Pacific Northwest - Riding out from ferry terminal in Seattle...

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I've got to ride up to REI early next week and I planned on taking the fairy over from Bremerton or Southworth. I was put under the impression that there are some trails that would take me there from either the Fauntleroy or Seattle terminal. Any ideas on how to make this ride without having to take main roads.
-Barry-
If you take a look at the Seattle bicycle map, there are some trails and roads to take you from the Downtown Seattle area to Fauntleroy. Part of the way is on a gravel path. To the Seattle terminal, all I know is there are a bunch of roads and maybe some bike lanes from REI.
http://www.seattle.gov/transportation/bikemaps.htm