By far our favorite hike so far is Little Si, located just east of North Bend.
Elevation gain on this hike is about 1500 feet, and the hike is about 5 miles round trip. We did this with our five year old, and it's a trail suitable for kids.
The trail offers a lot of variety: flat trails, rock-covered trails, slight climbs, a stream, even a wall for rock climbers. Top of Little Si was busy the day we were there, but plenty of room for a small snack and rest, as well as taking in views of Snoqualmie Valley, the Cascades, and Mount Si.
I highly recommend this hike. Can be completed in three hours even at a leisurely pace.