If you're staying anywhere near downtown, the ferries hardly seem like "getting out" since they leave from a pier at the south end of the waterfront, an easy and interesting walk from downtown.
• Take a Washington State ferry to Bremerton and back. Almost 2 hours on the water, in a place as scenic as the Aegean Sea, walk-on passengers a little under $6 round trip. (A commercial ferry, passenger-only, is a bit more expensive and aimed primarily at commuters.)
• Or, take the ferry to Bainbridge Island (30 minutes one way). Get off on the other side, walk about 1/2 mile into town for lunch or dinner, and walk back to ferry to come home.
Just getting out and driving around the area with no destination in mind can be a great experience, as the Seattle area, like most of the Pacific Northwest, is very scenic. If you'd like more specific destinations, try some of these:
• Two mountain passes, Snoqualmie Pass (follow I-90 east) and Stevens Pass (take I-405 to Highway 522 east, then take Highway 2 east) provide fantastic views. Of the two, Stevens is arguably the more scenic.
• Snoqualmie Falls (east of Seattle on I-90). The falls are scenic, and if you want to stay longer than it takes to just gawk, the Salish Lodge is pricey but incredibly romantic, with in-room Jacuzzis and fireplaces.
• North Bend (also out I-90) is the town where parts of the 1990 David Lynch TV series Twin Peaks were filmed. West of "downtown," there are hundreds of old railroad cars and engines quietly rusting away, with a cute railroad depot/museum closer to town. Rides are offered April - October, as well as a "Santa Train" in late November and early December.
• Roslyn is also out I-90 (not far past Snoqualmie Pass) and is where the TV series Northern Exposure was filmed. It holds many festivals including The Manly Man Festival, Pioneer Days, and Moose Days -- the latter is an annual Northern Exposure gathering held in late July. Might be worth a stop if you're out that way, or if you're a fan of the show, but it's a very small, quiet town without much to do most days. However, there is a great small museum in the downtown core right next to the Oasis Cafe. It is worth a browse as it profiles the city's coal mining past. Roslyn is worth the stop if you have the time!!!
• The Olympic Peninsula features beaches on the Pacific Ocean, Cape Flattery (the extreme northwestern point of the contiguous U.S.), and the only rain forest in America, the Hoh Rainforest. Other notable scenic areas on the Olympic Peninsula are Crescent Lake and Hurricane Ridge. You can take the Kingston ferry over from Edmonds and follow Highway 104 west until it meets up with Highway 101 (head north), or head south on I-5 to Olympia and catch Highway 101 West there. Doing the complete loop is a nearly day-long drive, and you could easily spend several days there, but you'll see a lot of fantastic scenery even if you never stop the car.
• Snoqualmie Pass - Summit and Alpental resorts on hour east on Interstate 90.
• Stevens Pass
• Crystal Mountain Mount Rainier
• Mount Baker North, near Bellingham).