Small, primitive campground next to Hwy 35 with access to Tamawanas falls
My family and I have stayed at this campground a few times, not because there's really anything special about the campground itself, but because of it's proximity to Tamawanas falls. The campground is primitive with a couple vault toilets, trash cans and sites with no amenities besides a fire ring and table.
If the campground isn't too crowded and you get to choose, pick a spot right on the East Fork Hood River. The river noise will drown out most of highway noise, plus it's nice to have somewhere to dip your feet, or body, after the hike to and from Tamawanas falls. The falls trailhead can be reached via the campground and the hike is moderate and well worth the work in my opinion.
Also nearby is the hike to Lookout Mtn, which we really liked. It was a bit more of a strenuous hike with lots of elevation gains, but the views at the top were well worth it. You won't be able to see Mt Hood and surrounding lakes like that from anywhere else.
If you're looking for a quick weekend spot to stay for a couple nights (max), that is close to some good hiking, but close to a main road, this place might be worth checking out.