A short ways south on Bothell Way from Lake Pleasant is De Landa Dog Inn. I've seen their sign from the road, and they are easy to find on Google Maps. Further east off of 522 is Paradise Pet Lodge. We left our small terrier there for several days when we flew back east. He didn't seem any worse for the wear!
Also in the area is Academy of Canine Behavior. We once looked at a rescue that they were trying to place.
That Bothell area is about a half hour drive from the Pier 91, assuming that's where you are going. I don't know about public transportation from there.
Last year relatives flew to Seattle for a cruise. They spent a night in a hotel near the airport. It's easy to get a shuttle from hotels in that area to the cruise docs. But I don't know anything about RV and pet boarding in that area.
