About 45 minutes east of Seattle is the town of North Bend. Looming behind is the forested and craggy Mt. Si (4167 ft/1270 m); generations of hikers in the Puget Sound area have broken in their boots on this mountain. It's steep (an elevation gain of about four thousand feet in four miles), but the reward at the top is a view of glaciated Mt. Rainier.
The trail can get crowded on sunny summer weekends, but if you can get up here mid-week, mid-summer, you'll get a bit of calm insight into the soul of Pacific Northwesterners--why they live where it's grey for nine months of the year: when 'the mountain is out,' no where else can compare.
Directions and trail info: http://www.wta.org/go-hiking/hikes/mount-si