dpratt, we always park at PreFlight Parking at TF Green. It's directly across the street from the airport. You park in your parking space, the shuttle meets you right at your vehicle, he puts your bags on the shuttle, and then drops you off at the door.
Here's their website:
http://www.preflightparking.com/PVD.aspx
It's $59.95 per week, but you'll see they have a printable coupon for 20% off which makes it $42.18 for the week. Not too bad.