Once a NYC cab goes to NJ, they have crossed a state line and the fares become way expensive. You also have to pay tolls. I would forget using taxi's as a means of commuting to/from NJ.

If you want to stay in NJ and commute, I would suggest the Courtyard in Jersey City, where you can get a PATH train nearby. Also, the Courtyard in Lyndhurst or the Renaissance Meadowlands (across the streee from each other) has frequent NJ Transist buses for about $3.00 each way that go to the Port Authority terminal. From any of those, you could easlily transfer to local NYC transit to your final destination.

Added: I just noticed that your dates are Friday-Monday. I would try to score some kind of weekend deal in the city (AAA rates are generally good).