Look for places at least an hour away from Seattle and Rainier. Also, go to wta.org, and check how many reviews and trip reports any particular place or trail get.

For a specific recommendation, there's a lot of beautiful scenery and generally pretty few people along Hwy 20. Once you get off the road, there are many beautiful creeks and lakes surrounded by miles of trails, and not that many people, especially early and late in the season (the highway is closed for winter, and reopens once the snow melts and avalanche danger is back to normal). Check out the area around Stehekin in particular.