Central jersey mostly exists in the minds of South Jersey people who don't want to be called South Jersey. Also I would not go by county as for Middlesex you have Piscataway that is most certainly North Jersey while areas like Dayton and Cranbury are certainly South Jersey.

I grew up in North Jersey and we considered every y linkthing several miles So. of 78 and No. of 195, South Jersey. Of course now that I live in the deeeeeeep South of Jersey, (cows, horses, meadows, tinier deer, farms, brackish Delaware river water) they down here consider Cherry Hill North Jersey. I argue and call that Central Jersey.
There is the North Jersey shore and the South Jersey beaches.
Bottom line is that it is all awesome and all expensive. It hurts to stay alive in this state, but we have EVERYTHING w/i an hour or two drive.
I'm from Jersey!
Holy hell your family goes back a ways in NJ 
MY family brought them a welcome wagon gift basket!