We live in Sequim, Washington on the north edge of Olympic National Park and Olympic National Forest (look it up on a map - you'll see where we are). I've been hiking, climbing, camping and fly fishing the park since 1969, and I know it pretty well. Things have changed dramatically over the past 20 years, and the days of driving up to a campground, in particular the ONP campgrounds and the Washington State Park campgrounds, and getting a spot on a whim are pretty much over. The same applies to the backcountry. It doesn't hurt to check because there can be no-shows.
Olympic National Forest does allow dispersed camping, and there are quite a few opportunities for that. An example is FS road #29 in the Sol Duc River Valley - look that one up to give you an idea. Another is the Hoh River Valley Road outside of ONP. We've seen lots of folks camping at virtually every wide spot or turnout.
If you need advice regarding specific spots you want to see, feel free to reach out to me for advice. One word of advice regarding the coastal section of ONP is that it is usually foggy during the summer. You can be socked in at your campsite at Kalaloch campground, while it's blue skies and sun just a couple of miles inland:
https://www.beachconnection.net/news...land101222.php.