Why has the man in the doorway come back to the old neighborhood after twenty years?
The reason that the man in the doorway has come back to his old neighborhood after so many years is that he promised that he would. He used to have a very good friend named Jimmy Wells. The two of them were just like brothers.
When they went their separate ways, they promised that in 20 years they would come back and meet again at the restaurant that was at the address where the man is waiting. So the man in the doorway, whose name is Bob, is waiting for Jimmy Wells to show up.
The man in the doorway in O'Henry's story "After Twenty Years" has come back to town because he and a friend made an agreement twenty years before that on that night hey would meet at the same restaurant. The restaurant is now gone but the man has returned and is awaiting to see if his friend will show-up.
I also believe the man has returned because he wants to see what had become of the man because he felt the man was inferior t him. He had gone on to achieve money and things in his life after he moved out west. He may want to brag about his life as he does so to the policeman he speaks with , that he does not realize was his old friend.
In the end of the story we realize who ahd made the better choices with his life and it was not the man in the doorway.