I was there a couple of years ago and would highly recommend the South side of the Skagit River. There was barely any traffic on it. It felt a lt like riding along the Tay in Perthshire.
From Anacortes I'd nip off the main road from Anacortes and head for Mount Vernon. Mostly to have breakfast at the Mt Vernon Cafe on Main St just over the Skagit River bridge. It's a super friendly old school diner. The guys there showed me an easy ride across town to pick up the road to the South side of the Skagit River just before Sedro Wooley.