I have resided here in Bayonne for nearly 5 years. It's kind of like a small town, Pennsylvania or Quasi Jersey Shore atmosphere in a geographically urban area. Everyone seems to know one another even if they don't, and you don't get that big-city hustle and bustle and exhausting pace. I am a native Bronxite and it's a real relief not to have to hear dogs barking all night long.
At times I think it is completely safe, but then I hear stories from people who live here and say that it's really deteriorated. I also here people late at night outside my building on West 32nd Street shouting and cursing at the top of their lungs. Despite a lot of police everywhere, a woman friend of mine said that she would walk the Avenues or Kennedy Boulevard at night, but not the sidestreets. Nonetheless, if you want a good deal for your money and want to live in a literal paradise in comparison to the Heights in Jersey City, Newark, or Elizabeth, Bayonne is your answer. There is a fantastic library and huge park by the bay with a nature walkway. No one should worry about walking around here during the day, especially in the south of the city by Staten Island or up in the high 20's, 30's, or 40th Street vicinities.