Twenty years earlier this had apparently been a different type of neighborhood. Bob and Jimmy had had a farewell dinner at a restaurant called 'Big Joe' Brady's. O. Henry wanted the neighborhood to be deserted for his story purposes, so he specified that the restaurant had gone out of business, the building torn down, and replaced by shops that closed early, including the hardware store where Bob is standing in the doorway.
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.”
Why did O. Henry want the neighborhood to seem deserted? Mainly because it would make Bob look suspicious to be standing there in the darkened entryway of a closed shop. Bob could imagine that the policeman would think he was a suspicious character, whereas the policeman only approached him because he was Jimmy Wells in uniform, coming to keep the appointment the two men had made twenty years ago. The reader would also think that the policeman approached Bob because he looked a bit suspicious.
Why did O. Henry emphasize that the weather was cold and wet? This would explain why Bob was standing inside the doorway rather than out on the sidewalk, which was why Bob thought that he looked suspicious. Bob also wanted to light his cigar, and he couldn't very well do it out on the sidewalk where it would be hard to keep a match lighted and where the cigar would get wet. But furthermore, the cold, wet weather explains why the plainclothes detective can approach Bob all bundled up in his overcoat so that Bob would not be able to see his features. The detective looked nothing like Jimmy Wells, as Bob could see when they got to some light.
About twenty minutes he waited, and then a tall man in a long overcoat, with collar turned up to his ears, hurried across from the opposite side of the street. He went directly to the waiting man.
We can understand why Bob might not have recognized the uniformed cop as Jimmy Wells, but to mistake the plainclothes detective for Jimmy Wells is asking the reader to accept too many mistakes. If the detective has his overcoat collar turned up to his ears and the street is dark, it is understandable that Bob might be temporarily taken in. But when they get to the electric lights in front of the cigar store, Bob balks:
“You're not Jimmy Wells,” he snapped. “Twenty years is a long time, but not long enough to change a man's nose from a Roman to a pug.”
Essentially, the place was deserted and the weather was bad because O. Henry wanted it that way. He realized that he could not have Bob standing in front of 'Big Joe' Brady's restaurant, so he simply tore it down and rebuilt the whole neighborhood. There is no one on the streets because all the little shops are closed. In the old days it must have been an entirely different type of neighborhood, with saloons and restaurants and lots of people coming and going.