I just parked at tue JFK raddison. Used airportparkinginc.com. $10 a day plus tax. Plus $5 fee. Total $59.44 for 5 days . its about 1 mile from the airport.
JFK long term is 4 miles away. And I am not sure about the shullttle schedule.
I called on my way over to verify when they have shuttles. They have every half an hour. I asked on the phone they should wait for me as I was in traffic. They said if there will be no other people waiting then they will wait for me. And they did. I will report back when I return.