From Neah Bay, it is a short 10 minute drive to Cape Flattery, the northwest tip of the Lower 48. The hike to get the to the tip where the Cape is located is only 1.5 mile through a beautiful Coastal Forest. Since Cape Flattery is on the Makah Reservation, you need to get a permit to hike the trail ($10 per vehicle for the year). We got ours at Neah Bay's General Store.
As for camping in the area, the options are limited. Hobuck RV Resort has 10 full hook-up sites with a seaview (but pretty close together) for $40/night. There is also a field down the road where you can camp for $20/night (access to shower and outhouses, but otherwise dry camping). It might be a good option on the off-season, but since we got there on the Friday before Labor Day, it was a zoo. The only other option was a new RV park called Hide-away RV park (that looked more like an RV storage lot than an campground), but they had full hook-up sites for $30/night (and a few dry camping spots for $20) and it was a short 100 yard walk to the beach. It was much more quiet there.
Keep in mind that the drive to Neah Bay from Port Angeles is pretty twisty and bumpy (frost heaves), so lock your cupboards and secure everything and take what you need for motion sickness. Take your time and enjoy the scenery!
There is a beautiful hike that can be done as an overnighter (you sleep on the beach!) to Shi-shi Beach or as a long day hike (it is part of the Olympic National Park). With Mara being injured (and with the amount of cars along the trailhead), we decided to keep it for another time.
Also, on a different note, I will publish cocktails here in some posts (you can find them in the cocktails category), but I won't publish them all (it's a traveling blog after all!), but you can access them all either on Instagram or Facebook with the hashtag redbusdrinks (#redbusdrinks). My friend Catheline is translating many of them and publishing them on her beautiful site (in French only).