x2 for Liberty Harbor. You are across the river from Manhattan and a ten minute ride on a PATH train (subway from NJ to NY) will get you to NYC faster than anything else. The PATH station is walking distance from the campground. Once across the river you can change to an NYC subway. bus, or walk to all attractions.
Forget Floyd Bennett Field. You do not want to take your RV or trailer on the city streets through Brooklyn from the interstate (495) on the north shore to get down to Floyd Bennett Field on the south shore. The streets are busy, tight, full of traffic and parts are what is considered in some sections of the country as "inner city". I have lived here all my life and would not attempt to do this in a trailer or RV. I am not sure what the NPS was thinking when they put camping sites in FBF with no limited access route that an RV or trailer is allowed to drive on anywhere near it.