Well, when you say home, I’m not sure if that means you are looking at condos or not. I would say take a look at Clifton, NJ. Near the delawanna train station.

There is a big condo complex there, and the single family homes match your budget. All walkable to the delawanna train station.

The commute is 1 hour to NYC.

The elementary schools are ok. The high school has a terrible reputation though. But there are county high schools. Magnet/charter or whatever. If your kids are good students they can probably get into one of those.