I know that the Hampton Inn which is right there on Route 1A near Logan, and the Four Points Sheraton do Park and fly rates - I had a friend do the Hampton and i think the nightly rate was 139.00/night with up to 14 days of parking
http://hamptoninn.hilton.com/en/hp/h...tyhocn=BOSLAHX
http://deals.fourpoints.com/Four-Poi..._112310_NAD_FM