If you are out for just a hike it is awesome. If you intend to fish it's catch and release. Above "Final Falls" there is a two trout a day limit. That location is about five mile up the trail from Green Canyon camp ground. Getting down to the river is hard in that area. In my youth we would use ropes to get down and back up.
The Salmon River used to be an fantastic steelhead river. It is also great salmon habitat. The river whole river has been closed to salmon and steelhead fishing for some years now. Below Final Falls is catch and release trout, but most of the fish are salmon smolts.
If you like hiking among old growth trees, steep canyon walls and clear mountain water it is the best around.
I did indeed intend to catch fish, though that did not go well. The river is all pretty fast by the hiking trail head and the hiking trail quickly departs above the river to where I did not want to hike up in my wading boots nor hang-glide down to the river.
All in all it was like you said, an awesome place - though I dont think i saw a substantial falls.. enough to be a "final falls". I was about a half mile up from the Green Canyon CG.
I was going to drive down the gravel road towards Salmon Beach and work my way back up river, but maybe another time.