Johnny Cakes' office was in Gatoville. That's an area of Key West where Mr. Gato started a cigar factory and built houses for his workers to live in. But by 1934 the factory had closed down and Johnny Cakes owned one of the buildings. I did not get to that part of town, but I did find this picture of the E. H. Gato Cigar Company. Maybe is office was in a building like this one.
Earlier in the book Beans calls Key West a thirsty city. Now it mentions bars and taverns on Duval Street. Full of Beans doesn't mention any of them by name, but a couple are mentioned in Turtle in Paradise. Here are some that are on Duval Street or nearby today.