Our last 2 trips, we flew out of Providence ON Thanksgiving Day (7 AM), and it was great...not very crowded at all. However, the long term parking was pretty bad...very full...from all the people who flew out in the days before Thanksgiving.
We had considered flying out the night before Thanksgiving to give us a little extra time, but don't want to ruin a good thing...the news reports are always horrid the night before.
We paid about $180 round trip the first year ('97), $240 in '99, $280 in '00, and $255 for this coming Thanksgiving. We always book sometime between February and April.