Why would you use a car service when you can hop on the subway?
Staying in Jersey City can save you a lot of money.
Lots of people wouldn't want to schlep to NJ via bus/subway/train (I think that's the order) with luggage. The hotels in that area of Jersey City are lovely (live 10 miles away, half of my family is from Jersey City, lots of my friends, attended graduate school in Jersey City, and I understand the close commute to NYC).
However, when I plug in the OP's dates, I don't get a low rate. Maybe you know of a site where they are much lower for those dates?
https://www.marriott.com/reservation/reviewDetails.mi
Personally, if the cost is the same, I'd rather stay at a small simple hotel in NYC than a nicer hotel in NJ. Maybe it's because I can be in the city within 20 minutes, so being able to step outside my hotel and be in the thick of things sounds great.