We live pretty close to this park and will occasionally spend a night or two at the campground. From the park you can access the Old Man's Cave trail head just below the loop located at the end of the road where the tent camping sites are located. This will enable you to see quite a bit of the park, including the upper and lower falls and Cedar Falls. Considering your bum knees and asthma, you should also check out Ash Cave, which is located a few miles from the campground, but it is still within the State Park. The trail is paved for handicap access and the cave is a short level walk back that is definitely worth the visit. Other sites within the park worth visiting is Conkles Hollow, Rock House, and the recently opened John Glenn Astronomy Park.
There are a handful of good places to eat in nearby Logan, Ohio. We really like Millstone BBQ, Hungry Buffalo, Maya Burrito Company, and Pizza Crossing.