I grew up central NJ and moved up to Hudson county 8 years ago. So anyway you go into the city add up all costs including tolls/parking for car, public transit per person including if you will need a taxi/subway to hotel from Penn station/PABT, and cost of time as rush hour here is no joke - if you drive in at the wrong time you can spend an extra 1-2 hours in the car. Also if you have never driven in NYC it may be the most stressful place you every drive. I have done it several times and only do it if I have no other option. There are tons of people in the streets, no right on red so very slow moving in Times Square area, you can't block the box, and traffic cops may show up at any time to suddenly decide no one can turn so you get rerouted in an instant, and the way some taxis drive you feel like you're in Mario Cart.
Times Square is convenient but it is noisy too. I stayed at a boutique hotel on a higher floor and they still gave you earplugs, and with the earplugs I still found it to be too loud. As I sit here I currently hear busses and firetrucks but the noise was non-stop and I did not sleep at all both nights. I always suggest staying outside Times Square in a quieter part of NYC or since you are in NJ staying just outside the city. PABT is at the outskirt of Time Square and Penn station just a few blocks away. In NYC all subways lead to Times Square as well and it will save you money to stay in a quieter area of the city both with hotel and parking. Believe it or not there are "timeshares" in NYC hotels too. My friend was able to get us a free night at a hotel once when we were in college using her parents unused timeshare points that they had that year. There are some hotels in NJ just outside NYC. I believe there is one in Hoboken, Weehawken, and they just built one in Edgewater. These are all a 15-20 min trip into Times Square. Seacaucus has a ton of hotels. Its less scenic in that area and the restaurants there are all chain places, but a good option if you are comfortable with the bus from PABT as they won't gouge you on parking like in NYC.