I have never heard "Bergen-Lafayette" uttered in the same sentence as the word "safe" unless "safe" was preceded by "not".
Journal Square is definitely a step-up from B-L, but it is still a bit sketchy in some parts of the neighborhood.
Of the three neighborhoods that you mentioned, The Heights is the best--by far.
However, you might want to consider Bayonne. While it is far from exciting, it is just a bit further from NYC, while being just one town south of Jersey City. And, Bayonne--overall--is definitely safer than Jersey City.