If you want to live in New Jersey, I would suggest Central New Jersey (I live in Sayreville myself), Middlesex Country or Northern Monmouth County preferrably.
Some good towns in the area:
Sayreville
East Brunswick (known for having a good school system)
Woodbridge
Edison
And all of these towns offer very good options to commute to NYC by train or bus.
We live in an apartment complex, and my wife's bus that goes to Wall Street comes right up our street, so she can walk out the door, walk for 2 minutes to the downtown NYC bus and she is there in no time.
Plus living in Central NJ you are approx 45 min from NYC, 30-45 minutes from the beach, almost 45-1 hr from Morristown/Parsippany area, 45 minutes from the Princeton/Trenton area, and about 1hr 20 minutes from Philly, and have very good access to all major roads in New Jersey.
So if for some reason you landed another job in the NYC or virtually anywhere in New Jersey, Central New Jersey is a good location commute wise.
Houses, decent ones at least will set you back 350K+ MINIMUM
Good 2 bedroom apartments will be 1200/month or more, depending on location.
PM me if you have any questions at all, would be happy to give you any information that might be helpful.