I made a happy discovery on a bicycle ride during one of those rare, sunny NW days when the temperature climbs to the 60s — my favorite bicycle path had been extended by four miles since last fall.
Whenever I ride on the eastside of Seattle, I try to include a spin along the flat Cedar River bicycle trail. The flat blacktop route heads toward the east to southeast out of Renton, but has ended in gravel about 6 miles out. From there to Landsburg, it wasn't made for thin bicycle tires.
This area of western Washington boasts many paved bicycle paths (maps are available online). Probably the most popular eastside trail is the Sammamish River Trail that runs between Redmond and Bothell. The Burke Gilman Trail runs between the Bothell area clean through Seattle. On the south side, the Green River Trail and the Interurban Trail connect Seattle with Kent and Pacific.
This is a great urban trail system, but my favorite is the Cedar River Trail that now connects Renton and Maple Valley. The bicycle path runs close to the hard-flowing river in places. Sockeye salmon swim upstream to spawn in the fall, and I've seen bald eagles perched in trees along wooded streambanks.
The trail uses the abandoned Burlington Northern Railroad right of way sandwiched between the river and busy State Route 169. The King County Department of Natural Resources and Park plans to eventually pave the path all the way beyond the suburbs to a park in Landsburg.
When complete, that path will take cyclists past Maple Valley to the uncongested rural roads in the Cascade foothills.
I've compiled more free bicycle route maps for Washington at Washington – Free Maps.