Rent goes very roughly 25% cheaper than Manhattan for similar digs, everything from basement studios (~$1500) to modern luxury towers, and gets cheaper with more distance from the PATH.
Bonuses: You dodge the NYC income tax (over 3% of income). NJ sales tax is a bit less too. And NJ has easier driving and flying (Newark) access to the rest of the world.
I've lived on the NJ Gold Coast and commuted to Manhattan for basically my entire professional life, and quite satisfied with that. I've never lived in any other area than NJ/NY so can't compare it with the west coast.