It takes 15 minutes or less into the city and so Liberty Harbor is convenient. It costs $2.50 to get into the city from Liberty Harbor and $2.50 to get back there on the PATH. The PATH will take you to either the World Trade Center or Times Square (33rd St).
LH is convenient enough that you don't have to eat your meals in the city, you can eat breakfast, grab a snack and get back to fix dinner in your own "home".
Also, the views from Liberty Harbor are just magnificent with the Statue of Liberty within view, as well as the skyline.
When making your decision, you need to weigh the costs of transportation and convenience with the expense of the campsite. If you don't mind spending an hour to hour and a half commuting each way, then by all means, save the costs associated with the campground. Also weigh in the costs associated with the commuting. I just figure my time is worth much more than that, especially if I have been walking around the city all day.