Great question! According to the Encyclopedia of New York City, (2d ed), the Commissioners' Plan of 1811 laid out the Manhattan street grid up to West 155th Street. read more
The Macombs Dam Bridge runs from 155th street in Manhattan to roughly 161st Street in The Bronx. And at the north end you can see the Broadway bridge run from 220th street in Manhattan to 225th street in The Bronx. Seems that the intention was to continue the grid into The Bronx. read more