Beyond the Seattle-area, and even Washington State, there are many amazing areas within a day's drive. But there's no need to drive. You can get to nearly anywhere in the state by bike. This page is an ever-growing guide for Puget Sound regional rides, and the best ways to get there.
Seattle to Mukilteo Ferry Terminal - from Mukilteo, you can take the ferry to Whidbey Island, itself a fun place to ride, and you can connect to the Olympic Peninsula or even Canada via Whidbey. See the complete ride-through for more information.
Once you arrive at Clinton on Whidbey Island, there's plenty of scenic back roads to connect to Keystone (ferry to Port Townsend on the Olympic Peninsula), Oak Harbor, Deception Pass, and Anacortes (ferries to British Columbia and the San Juan Islands). See the ride-through for the route as far as Oak Harbor (under construction).
Here's a good trip report from Bike Overnights that highlights a loop route from Seattle to Whidbey Island with a stay at Fort Ebey State Park, returning via the ferry from Kingston to Edmonds (there's also another report that covers Edmonds to Pt Townsend for a similar route) and back into Seattle.
Trails near Whistler, British Columbia, Canada
Anacortes and San Juan Islands: It's easy and cheaper to avoid the car wait for the ferries from Anacortes to the San Juans (or Sydney B.C.) by taking a bike to the islands. Nearly all of the major ones have excellent bicycle routes.
If don't want to take the ferry, you can do a nice loop of around 25 miles, with rolling hills, including a visit to Deception Pass. Below is an example route.
View Anacortes Loop in a larger map