In NJ, most schools are pretty good and well documented.

NJ is a funny place with diversity; there are places with excellent cultural diversity and places with excellent economic diversity; there are almost none with both.

Your mode of transportation matters when considering where you work in the city. If you’re uptown, find a bus terminal since the vast majority of commuter routes take you to the PA bus terminal. If you’re downtown, look for a train line that takes you to Hoboken where you can hop a PATH train or Ferry. If you’re midtown, look for a train that gets you to Penn Station. Few actually works around Penn Station, so while popular, it’s mostly a way station to other points.

Your price range is decent, but probably won’t get you walking distance to a train station in one of the bigger towns. I recommend you look at towns along major commuter bus lines if you’re uptown. Passaic county highlands and surrounding area is a fave since it has an express bus terminal in town, the schools are good, and you can get that classic Americana style housing there. A lot of NY expats either love it or can’t handle it. Their brains tend to melt at mountain forest communities with lakes bears and bald eagles everywhere.