Peakbagger covered the options well. There are a fair number of commercial campgrounds scattered about, but most tend to be RV orientated.
Arethusa Falls is pretty neat. It's a very popular day hike, about a 3 hour round trip, plus whatever time you spend hanging out there. I need to remember to hike up there in the spring when the water is really raging.
While not quite as impressive as Arethusa Falls, the Nancy Cascades on the Nancy Pond trail a couple of miles south of the Arethusa trail head on RT 16 is pretty nice with a lot less traffic. If you go all the way to Norcross Pond, you get rewarded with a nice view. It's about a 9 mile round trip which takes most of the day, but it's a reasonably easy hike.
If you like waterfalls, while at Pinkham go over and see the Glen Ellis falls too. That's a short walk.