Depends on what you consider "long term". They do offer a package for a 1 night stay with 14 days free parking, or 1 night with 5 days free parking, or 1 night with 8 days free parking. There is complimentary shuttle service to/from JFK available 24/7.
I tried calling Reservations to ask about an early check in as our flight arrives at 6.40am and they say we can't check in until 3pm - anyone know how we can organise an early check in or at least a day room until our room is ready - not getting any help from Radisson.
I have found that if the property was not sold out the night before they will be accommodating if you arrive early. You will not get to the hotel until 8:30 or 9:00. If you are not I suggest that you become a member of the Radisson Club Carlson which is their guest club. It might help a little.