Both times I took the train into Seattle, stayed at the HI hostel in town, took the ferry the next morning and then rode to intersect the NT a little ways east of Anacortes. The first night I stayed in some state park (think it was called Kitsap). Second night at Fort Worden. Third night at Bayview State Park, which is on the route. between Anacortes and Sedro-Wooley. At the time, most of this in on AC's Pacific Coast Route and may still be. Not the most scenic of routes, but convenient. And I got to hang in Seattle.
On that tip, for those wanting to ride from Seattle to Anacortes, this is what we did last year: We headed north through Seattle neighborhoods and then caught the Interurban Trail North on the north side of the Ship Canal. This trail mostly follows an old rail line and winds its way through the suburbs to the north. It's pretty well signed though meandering at points. We got off the trail outside of Everett and rode to the Mukilteo Ferry Terminal, and caught it over to Whidbey Island. Whidbey Island is pretty with lots of hills. We mostly used SR 525 north towards Coupeville, then used the ACA Pacific Coast Route, Section 1 to get to Anacortes. (SR 20 is less hilly, but the ACA route avoids a particularly unfun section through Oak Harbor.) Camping can be found at South Whidbey Island State Park and Deception Pass S.P. Or, if you are on warmshowers, you can stay at the "Bike Shack" on the south part of Whidbey.