Hocking Hills is a nice campground but expect it to be packed and noisy. I have not been there since they renovated the campground and converted a lot of sites to FHU, but if you want a level site without a huge drop off from the pad forget it without a scout trip, not many exist. The campground is on top of a narrow ridge and the hill coming up is very interesting. The 3 times we were there the sites were dirty with accumulated trash and dogshit which we had to pick up from the previous user. They had multiple camp hosts that appeared to do nothing but ride around in golf carts or Gators.
In mid June unless its a wet spring the waterfalls will be down to a trickle. Most of the cave areas are probably not something you want to access with bad knees, maybe Ash cave which has level access but about 1/4 mile hike. Take everything with you as there is not much in the way of stores and its a fair drive to Logan.
Hopefully during the reno they moved the dumpsters which were scattered all over the campground. Hope your site is not next to one of those as they would be overflowing come Sunday afternoon and are emptied at 5 AM Tuesday. Another thing is the campground has a large raccoon population, so do not leave anything out or they'll have it.