Storm surge is often one of the more dangerous and costly aspects of a landfalling hurricane. It occurs as the extremely low pressure found at a hurricanes center literally bulges the ocean's surface upwards, and then the hurricane's strong winds force that water inland, leading to significant flooding.
However, remember that winds flow counter clockwise around any area of low pressure in the northern hemisphere, and hurricanes are no exception. Because of this, the magnitude and intensity of a hurricane's storm surge varies greatly depending on the path of the storm, and where a given location is situated relative to the center of rotation.
In particular, for storm surge to be maximized, winds would have to be directed on shore. For a north moving system making landfall on an east-west oriented coast line, storm surge would be worst in the storm's northeast quadrant. Likewise, storm surge would be minimal in the storms northwest quadrant, as winds would be directed off shore. In many cases, this would even lead to sea levels falling.