Hi @Ligia Ulloa
I can't really caution against certain areas, but I would recommend looking into what Bayonne leaders "would like" to do. http://www.bayonnenj.org/Articles/Read.aspx?id=925 is great reading for the city's master plan and will give you insight into the future of Bayonne to allow you to buy into areas of progress (if that is your desire).
What I like about Bayonne is that there are areas for just about anyone. The progress I've seen to date has bee positive (Costco, luxury apartment builds, bike share, park improvements) and the progress announced has been exciting (ferry, additional luxury complexes, trolly, commercial development for higher streets, warehouse jobs, connected parks). For renters working in Bayonne, there will be warehouse, commercial and medical jobs to name a few. For those working outside of Bayonne, the light rail and bus system are robust for easy access to Jersey City, NYC, Newark and more. On top of this, it is a very walkable city with great parks and access to water (Hudson River or Newark Bay) and a cruise line.
As a heads up, Bayonne will be going through a tax revaluation shortly. Depending on the results, prices and profitability ratios may change slightly depending on how each house's appraisal has appreciated vs. the average. This doesn't scare me off, but it might for others depending on levels of risk aversion.