Welcome to Seattle. I've been here for almost 30 years but have fairly recently gotten back into cycling.
I used to go to Vashon Island (I eventually lived there for 10 years) and ride. It is pretty popular with folks because it is so rural yet close. It is a ferry ride from West Seattle. I believe there is still a downtown Seattle walk-on ferry. It is best to get a map and stay off the main road Vashon Hwy.
Have you check out the Cascade Bicycle Club yet? They have tons of rides.
Have a great time exploring the beautiful areas.
http://www.wsdot.wa.gov/ferries/
Carole