The setting for "After Twenty Years" is a good one because the story has to take place in darkness. It is only because of the darkness that Bob doesn't recognize his old friend Jimmy Wells. If they had met in a crowded restaurant, Bob would of course have recognized Jimmy in his uniform and Jimmy would have immediately recognized Bob as the man who was wanted by the Chicago police. In that case, Jimmy would not have been able to get a plainclothes detective to make the arrest for him. Jimmy would have been in the awkward position that O. Henry was trying to avoid. There would have been a big scene in which Jimmy tried to arrest his old friend and Bob tried to talk him out of it. This kind of a conversation could have gone on for a long time. The story--however it ended--would not have been as neat and compact as it is now. One of the admirable things about "After Twenty Years" is that it covers so much time in so few pages.
If Bob and Jimmy had met inside a crowded, and brightly lighted, restaurant, Bob would have had no need to explain what he was doing there. Much of what Bob tells the cop, whom he doesn't recognize, is really intended as exposition for the reader's benefit. The reader would have no idea of what was going on if the two men met inside a crowded restaurant. The reader would not even understand that they had made an agreement twenty years ago that they would meet there. It would have to be an entirely different story with entirely different dialogue and an entirely different ending. Jimmy might not even arrest Bob. Bob might be able to talk him out of it, since Bob is obviously a good talker. On the other hand, Jimmy might try to arrest his old friend and Bob might put up a fight in a crowded restaurant. O. Henry obviously did not want to get involved in describing that kind of imbroglio.
O. Henry obviously thought that such a meeting between old friends should have taken place in a big restaurant. That is why he includes the exchange about 'Big Joe' Brady's restaurant, where the two men parted twenty years before.
“It's all right, officer,” he said, reassuringly. “I'm just waiting for a friend. It's an appointment made twenty years ago. Sounds a little funny to you, doesn't it? Well, I'll explain if you'd like to make certain it's all straight. About that long ago there used to be a restaurant where this store stands— ‘Big Joe’ Brady's restaurant.”
“Until five years ago,” said the policeman. “It was torn down then."
The two friends had fully expected to meet in a crowded restaurant, but ended up meeting in front of a darkened hardware store because many things change in twenty years. That is the theme of O. Henry's story.