We have flown out of JFK many times, and we live in central NJ. From here, it is not that bad to get to JFK, we take the outer bridge crossing thru Staten Island. (My north Jersey relatives have to cross thru Manhattan, and that is NOT a great option, so they avoid it.)
We always park at Avistar now (the long term lot is not great, esp when you return late at night).
We used JFK for cheaper air (there are 6 of us), and to use JetBlue and Song. (now of course Song is gone and JetBlue available out of Newark). We got $59 each way on Song many times to Orlando.......... much less then we could get via Newark. We now use Atlantic City when air is reasonable, and we can use Southwest out of Philly.