More (if not the whole thing) of the New York, Westchester and Boston Railway would had been integrated into the New York City Subway. The 5 train would extend all the whole to White Plains on the western branch and Portchester on the eastern branch. One can make a bet that public transportation in the Bronx would slightly better than the deplorable condition it's in at the moment.
Since Westchester County was predominately rural well into the twentieth century when you had lots of suburban development and highways laid down, you can bet on it having a character similar to Staten Island. It would be wealthier, predominately white (depending if white flight doesn't just bring people running into Putnam and Rockland County), and a purplish county (with the OTL Bronx being pro-Democrat and Westchester being pro-Republican) that could swing either way on the election. Very Republican but slowly becomes more Democratic.
An expanded Bronx would include Playland giving Coney Island a run for its money as New York City's main amusement park. I wouldn't expect Freedomland to come about with a popular and close amusement park already in the area.