I use a similar place called Avistar Parking. They're located 120-34 So. Conduit Avenue. You drive their, they valet park your car and someone puts your bags on a shuttle bus, then helps you off with your bags when you get to your terminal. When you get back, you call them on your cell phone and they come pick you up and take you back to the lot, where your car has been brought right near the exit and is waiting for you.
You can print a coupon from their web site and it's $17.50 per day (plus tax and a $3.00 per stay "fuel surcharge").
I used to use the long term parking on Lefferts Blvd, which is a little cheaper, but the hassle of driving around looking for a spot, the having to schlep your bags from the car to the AirTrain then to your terminal is annoying. To me the valet service is well worth a few extra dollars.
Long-Term Parking