Well, we needn't have worried. It turns out that August is cherry season, and bears in cherry trees were easy to find. In fact, we saw five bears, none of them on the ground. What was on the ground was cherry pit-laden bear poop! The bears paid no attention to people, even when a horde of tourists was standing under the tree.
Indeed, most of the wildlife seemed rather tame. We saw many turkeys and deer (deer 1, deer 2) in both fields and woods. They hardly bothered to move away unless we were very close. We even saw a slightly scruffy red fox crossing the road in the middle of the day.
There were songbirds and reptiles also. The birds were uniformly dull-colored (mostly dark-eyed juncos), but we did see a nice box turtle and even a garter snake at the very top of Rich Mountain (only 4000 feet high).
The one big game animal that we almost missed is the elk, relatively recently reintroduced into the park (there were none in 1962). We stopped at the visitors center on the Cherokee side of the park just before leaving, and just as we got in the car, a herd of elk moved out of the woods into the adjacent field. I didn't have a long lens, but one can still see the yellow tags on one elk's ears (do they really need to do that?).
Then we were off to Atlanta for more civilized entertainment! Here we are at Stone Mountain outside of Atlanta, but that's another story.