The N. Fork is gorgeous. It's not easy to fly fish, however. I found it challenging to access the water via sporadic riverside trails. Wading can be tricky because the water is swift and deep in many places. Highly braided surface currents can make getting a good dry-fly drift difficult as well.
After wearing out my arm casting dries and coming up empty, I had some luck bouncing a heavily weighted nymph (GRHE) along the bottom of the moderate depth runs. Hooked up with a few hard-fighting rainbows in the 10-12" range. According to a guidebook, the 'bows commonly reach the 14-inch mark in the Sko.
I talked with another fisherman who said the fishing improves and the water becomes friendlier the further you're willing to hike. I believe the NF Skokomish Trail infilitrates 15 miles or so into ONP backcountry. Might be worth investigating if you've got some time and a sturdy pair of boots.
Good luck if you go. Let us know how you do.