There is a new Red Parking garage just outside of the new T8. Simply park, lock your vehicle, and walk across the street to the terminal. But, it's quite expensive ($33/day).
A less expensive option would be the Long-Term Parking lot at Lefferts Blvd, for $18/day. Just follow the signs to get there, park, and then take the free AirTrain to the terminals. The Long Term / AirTrain option adds only about 15 minutes over driving to the garage outside T8. IMHO, it's really worth it to save the cash! (especially if you are staying for a while).
Using Long Term also makes for a MUCH faster exit from the airport upon your return, since the payment booths at the T8 garage can get very backed up soon after the afternoon widebody arrivals. I've had times where it has taken 20 minutes to get out of the garage, about DOUBLE the time it takes to ride the Howard Beach AirTrain from T8 to Lefferts Blvd, pick up my car, and clear out!
More info about JFK parking
HERE.
Hint: when traveling out of T8 and using the AirTrain, take the train from Lefferts Blvd to T1, then get off and walk across to the other side of the platform and take the "All Terminals" train one stop T1 -> T8. It saves a good 7-8 minutes over going all the way around to all the terminals.