A lot of the Obama swings are due to Sandy, no doubt. But it could be a result of NJ being younger than average and ethnically diverse.
Now my question for someone who has never been to NJ, why is NW NJ very Republican?
This is actually an important point. The bigger swings to Obama, as I pointed out elsewhere, were not in areas heavily affected by Hurricane Sandy but rather than in minority-heavy cities and suburbs of North Jersey: Hudson, Passaic, Union and Middlesex Counties.* That suggests that at least a significant part of the swing was Obama's general, nationwide improvement among Hispanics and Asians rather than the result of Sandy, though Sandy certainly played a role as well.
*Essex County is missing from that last, but Essex is more black and less Hispanic and Asian than the those four, which may have played a role in the magnitude of the swings. It did still swing to Obama, just less.