I want to add Staten Island to your list. While it is not in NJ, it is immediately across the Outerbridge, Bayonne Bridge and Goethols Bridge from 3 entry points to “Central NJ”. I the largest Jewish community there (Willowbrook) is located directly adjacent to the Staten Island Expressway, and is a 5-10 minute drive from Bayonne, Linden, and Elizabeth NJ.
As for the other concerns….
Staten Island is a highly diverse “out of town type” community within NYC. There are Chasiddish, Yeshivish, MO, and other kinds of Jews all living together , often davening together, and working on various community events and chesed projects together. There are two main elementary schools locally, RJJ (which has a seperate boys division, girls division, and preschool) and well as JFS which is a co-ed school. JFS and RJJ Girls, share a campus although they are completely separate from each other. There is a Chofetz Chaim HS and countless ES and HS options just over the bridges with busing in Elizabeth, Brooklyn, and West Orange Mainly (people also send to Teaneck and Passaic among other places for HS) (more info on Staten Island Schools here https://www.theyeshivaworld.com/news/uncategorized/1658207/staten-island-offers-multiple-school-options-for-the-jewish-community.html).
In terms of affordability, the initial cost of housing is higher than many places in NJ but cheaper than most of NY. The trade off is that property taxes are much lower than NJ. Also the cost of schooling, shul memberships, and general life styles are also cheaper in Staten Island as the lifestyle is a more laid back one with less emphasis on money. My wife and I moved there 5 years ago due to circumstance, thinking that it would be a stop on our way to elsewhere but we have fallen in love with the community.