For us, it depends on what time the flight to JA departs. When it is earlier than 7am, we remove all stress by staying at the Renaissance Hotel(pretty posh, in a Phillipe Starck way) the night before for $109 for a king suite, which includes parking for the whole time we are away! We just wake and roll to the lobby where the 24/7 hotel shuttle whisks us the 90 seconds across the interstate to the East Terminal. When we return, I call them before getting to Immigration/Customs and the shuttle is there waiting for us...
When the flight departs later than 7am, we generally just drive ourselves to a certain pay lot that is literally a stone's throw from the airport. We get the aviator parking rate, which is about 1/2 price. The only bad news about this lot is, if you park in the lower section and are gone for more than a couple of days, the grime from the interstate settles on your car creating.....ick...
