Storey Burn Trail and Gales Creek Trail Loop
The Storey Burn / Gales Creek loop is a hidden gem in Tillamook State Forest. Given its proximity to the city, it is a relatively low-traffic trail where you can still find some semblance of serenity even on a weekend (in the winter). You'll get sweeping mountain views, a waterfall, and some stream crossings. It's a great, variable hike.
You will share the trail with some mountain bikers, but they're used to hikers. After going under the Graham Bridge, you'll likely be greeted by the popping engines of OHV's on the Spencer Trail.
Park at the Summit Trailhead (large sign off route 6), and walk to the eastern-most side of the lot to begin at the Gales Creek Trail.
This would be a tough trail for children. There are some steep climbs / dropoffs and a crossing at the falls.