Use Pre-Flight Parking in Chelsea. If you reserve and pay in advance you get a rate of $15 or so per day, every seventh day free. You just have to reserve and prepay one day to get that rate for a stay of any length - so if you run into really bad traffic and have to park in the airport to make your flight, you're not out a lot of money. They also have a frequent parker program that gives you a free day for, more or less, every paid week.
(I have no economic or other interest in PFP. I'm just a happy customer.)