Since you are an "Iambusy" person, I assume you only wish to check the things out quickly. If I were you, here I would do:
The first day: since you stay near the airport, go to Mt. Rainier first, it could save you one hour drive either way.
the 2nd day: visit Seattle, buy a city pass, or do whatever you'd like. In the evening, take a ferry to Bremerton, on the ferry you not only will see the Seattle skyscraper and beautiful Puget Sound on one end, but could enjoy a sunset in the Olympic mountains on the other end, if you are lucky enough.
the 3rd day: visit Hurricane Ridge if it's open (open only weekend until May 30th), next drive by the Crescent Lake, and last, go to Sol Duc to hike a short distance and see the Falls and typical Rain Forest environment. No need to drive all the way to the west entrance, Unless you want to see the town of Forks, the famous vampire territory.
the 4th day, sign up a full day whale watch at Port Townsend. This trip not only gets you to see orcas and whales, but also take you to the renowned San Juan island, and stops at the Friday Harbor for two hours. This boat trip will immerse you into the typical but the most beautiful Seattle islands and Sound views.
Well, this April and May Seattle has had unexpected sunny weather all through. Wish you have a good trip!
