Once you’ve crossed to Clinton from Mukilteo, you can head directly NE on 525, but I recommend a side trip to the charming little village of Langley. It is less direct, but you can make a loop without having to backtrack.
There are other roads that more or less parallel 525 to the east and west. This is the option I took as 525 can be busy on weekends, especially the deluge of cars that come through from the frequent ferry landings. When you reach highway 20, take a left towards Fort Casey. Despite the ferry traffic, this is a lovely ride.
At Fort Casey, purchase your ferry ticket from the machines inside. There is a choice for bicycles. When the ferry arrives from Port Townsend, queue up with the walk on passengers as you will be allowed to board before the cars.
Follow the instructions of the ferry employees. Usually, you park at the front of the ferry and you can tie your bike to a rope, but it’s not really necessary as it’s not a rough trip. The ride is only about 45 minutes, and then you find yourself in the beautiful town of Port Townsend.
There are a few Warm Showers locations in Port Townsend, but they involve steep hill climbs. For the short visit, I recommend staying right downtown so you can enjoy walking the main street and all its shops and restaurants.
The next day, you will ride to Port Angeles.