While there is no park host, the campgrounds are pretty close to the road. With that, there is plenty of road noise and the trail down to the river goes right through 4 campsites so privacy is minimal.
With just seven campsites, I liked the feeling of seclusion you might get similar to the dispersed sites further down the road, while still having a relatively clean pit toilet and garbage available. Kind of the best of both worlds. I also liked that it was $15 (vs the $20 of Henry Rierson nearby). It's first-come, first-served, and sites really do matter, so it's worth looking around or coming early or before the weekend to make sure you get a good one. Site #1 is literally a small turn-out on the road and worth avoiding, while other sites (like 4/5/6) are much larger, more secluded, and on the water. Sites 5 and 6 are also perfect if you have a group and want to share/go back and forth between the two sites. Site #7 is another one that's right on the parking lot and fairly small and worth avoiding if possible. I'd probably give this one a 3.5 star rating since the larger sites are nice, but not a ton to do other than hang out in/by the river.
Out of Morrison Eddy, Henry Rierson Spruce Run, Nehalem Falls and Cook Creek, Beaver Eddy should probably be the last campground on your list. There are a couple of nice sites, with an open feel and parking area, and a good hike possibility with Cougar Mountain Road across a nearby bridge. And the water and forest views are smile-inducing. But the road is incredibly adjacent, privacy does not receive good overall marks here and there are still inconsistencies about whether it’s open or not at any given time due to nearby logging.