New Jersey is a fairly safe place to visit. Suburban and countryside areas are very safe along with most Jersey Shore towns. Cities are mostly safe but do exercise common travel sense. Some neighborhoods of Camden, Newark, Atlantic City, Jersey City, and Trenton are crime prone but it is unlikely that you will visit these areas. As in most US cities, when out at night, stay in well lit and well trafficked areas and you will be fine.
New Jersey has the highest density of car ownership in the United States so expect crowded highways and the occasional irate driver. Many major highways are under construction for expansion purposes, resulting in delays. Traffic tends to move well above the speed limit on the New Jersey Turnpike, The Garden State Parkway, or other highways and you can expect to be tail-gated when driving in the left lane. Best to stick in the middle or right lane if you don't like that sort of thing.
Under no circumstances whatsoever are you to import firearms into the state. New Jersey does not recognize any out-of-state gun licenses and there are no gun offenses that are graded below a felony. Police are known to enforce these laws vigorously, and if caught with a firearm you will be prosecuted, even if you are just a hunter traveling through.
Also, it is illegal to import fireworks into the state unless they are mandated by a municipality for special occasions to be attended by the public at a park or on the shore i.e. Independence Day. However, you'll find that this is worked around quite easily - it is impossible to cross the border into Pennsylvania and not see signs for on-the-border fireworks shops.
Although the media and other sources portray residents as "rude" and "loud," most natives are proud of their state and are more than willing to help a tourist with directions and other tips. Don't hesitate to ask for assistance. Some areas - especially the famed Jersey Shore - are very used to tourists.
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People flock to New Jersey from all over, especially from New York City and Philadelphia, making it difficult to isolate the New Jersey accent. The true New Jersey accent is evident in native speakers like politician-turned-broadcaster Steve Adubato, United States Supreme Court Justice Samuel Alito, and Louis Freeh, the former director of the Federal Bureau of Investigation.