Whidbey Island.
Whidbey isn't as "remote" as, say, the Olympic Peninsula, but it sure is purty. Natural splendor is Whidbey's middle name. It's nowhere near as built-up and gentrified as Bainbridge, but it's not quite the hinterlands either. You won't quibble, once you get here.
Start early in the day. In Seattle, catch a # 511 Community Transit bus on 4th Avenue and then transfer to a #113 at the Lynnwood station (Bay 3B). The #113 will drop you off right at the ferry dock.
I think you can also take Amtrak to Everett in the morning and then, at the train station, (easily) find the #18 Everett Transit bus, which will get you to the ferry.
(Check this info, OK? Bus numbers can change over time...)
The ferry runs from Mukilteo across to Clinton every half hour.
On the Whidbey side, for much of the day (but never on Sunday), there's FREE bus service. (The buses don't run as often as Metro buses, so be sure to grab a schedule.) Get on a bus at the ferry terminal, and then just ride around and sightsee until you figure out where you want to get off. Ask the driver for suggestions. Go to Langley or Coupeville if this is your first trip.
Maybe you should bring enough cash for a taxi in case you forget to get back to the Clinton ferry doc before the buses stop running. (You won't find a lot of marked bus stops. Best to know approx. when the bus is coming and then stand at the side of the road and flag it down. Bring a flashlight.)
Check the weather reports. It's often 10 degrees colder than Seattle, and often more rainy and windy. But there are lots of beautiful blue-sky days too.
Once you travel up to Whidbey once, and see how easy it is, you'll want to do it regularly.