For what you might save on room charges, you will burn in taxi fares and tolls, as well as you own time.

I have never taken a cab from Manhattan to Jersey, but have often used them to go out to Long Island. Once the driver crosses the Queens/Nassau line, he makes note of the fare on the meter, and beyond that point any additional fare to your destination is doubled. This is permitted since he can't pick up a return fare in Nassau or Suffolk.

I believe the same rules will hold for travel into NYC, other than perhaps to/from EWR, where different rules might apply.