In this story, we are never told why Bob went to Chicago in particular. We are told that he went to "the West" in order to find his fortune and to have adventures. These can be seen as two different reasons.
Bob wanted to leave New York partly to make his fortune. This is clearly stated in the story when he talks about the night he and Jimmy last saw one another. He says
The next morning I was to start for the West to make my fortune.
This tells us that one reason he had for going west (and perhaps to Chicago) was that he thought he could make more money there than he could in New York.
But money is not all that he was after. He seems to have felt that New York would not be interesting and exciting enough. He felt that life in New York would not be enough of a challenge to him. He shows us this when he says
A man gets in a groove in New York. It takes the West to put a razor-edge on him.”
These lines show us that Bob went west, and ultimately ended up in Chicago, to make money and to find adventure.