Are you looking for turnkey properties (tenants in place, renovated in last 10 yrs) or are you more interested in properties that need work and potentially don't have tenants in place?
I actually live in Bayonne and I see the growth and value there but the property taxes tend to crush most of the cash-flow potential. Rents are strong and it's becoming more of a relocation destination for the NYC/Brooklyn type clientele. There is currently some competition with a few new luxury buildings and more on the way but there will always be renters for product that falls at a price point below what the new luxury buildings are asking. Offering parking is a huge value add in Bayonne and really any JC neighborhood. West Bergen is a JC neighborhood that has really strong growth and tons of new development. New retail has started opening up and more modern national operators are slated to open in the near future. Starbucks, Five Guys - and Target and Stop & Shop are coming soon. Taxes are pretty normal over there and it's on the safer end of the spectrum. Lincoln Park is pretty amazing and it's very well maintained.
Bergen Lafayette and Journal Square/McGinley Square are both getting crazy with prices and JC Heights is probably the most desirable and the most expensive. Downtown JC isn't really an option unless you plan on doing a condo conversion.
Greenville gets kind of a bad wrap but rents are strong in certain pockets of Geenville and as long as you offer a good product with desirable layouts/amenities you'll be able to command strong rent and get good tenants. There are some sections of Greenville that can get a bit dicey so best to understand the landscape before jumping in..
Happy to answer more specific questions on neighborhoods! Hope the above helps