Recreation.gov
First: You’ll need a map of the Olympic National Park/National Forest. You can write to the Olympic National Park, Visitor Center in Port Angeles, WA, and request a map. On the other hand, if you live reasonably close to Port Angeles, take the time to visit with the Wilderness Information Center inside the Visitors Center. By doing so, you can get more information more quickly: call before you go.
The Park map, small as it is, contains all the trails, trailheads, primitive trails and National Forest trails that will deliver you to the National Park trails as well. The Olympic Wilderness Trip Planner will identify trailheads, mileage, campsites and the intersections of trails.
Next: Foremost, anyone intending to backpack into either Olympic National Park of Olympic National Forest must get a Wilderness permit. All the information you need is at: https://www.recreation.gov/permits/4098362. Pay close attention to the reservation areas in the Park. Areas outlined in red ink, as well as camping sites identified by red triangles, restrict the numbers of campers allowed on any given day during the backpacking season. All the information needed is also at: https://www.nps.gov/olym/planyourvisit/wilderness-map.htm. If you haven’t requested or haven’t received a map you can see the maps at: https://www.nps.gov/olym/planyourvisit/wilderness-trip-planner.htm.
Finally: After talking with the Rangers at The Wilderness Information Center, then review the maps and select your hike of first choice. Next, identify a back-up hike in case your first choice isn’t available. Do this via: Recreation.gov https://www.nps.gov/olym/planyourvisit/wilderness-trip-planner.htm. If you succeed, your hike of choice is yours.
If, however, you didn’t succeed, return to recreation.gov using the link above and hopefully your back-up hike will be available. If not, pick a new hike and try again.
In my Book “Loop Hikes in the Olympic Mountains” there are numerous loop hikes. A number of them have unlimited camping space; but remember, you’ll still need to apply for and secure the hike via Recreation.gov. Another piece of good luck for fording rivers, if you choose to do so –the snow pack this winter has been as skimpy as I’ve ever seen. Snow melt-off looks like it will be over by June. The flow-rate on rivers dependent on snow-melt will be low this summer. Read my book and you’ll get a feeling for length, difficulty, trail conditions, elevation gain/loss, water availability and places you might not have ever visited.