We went last year on Sunday/Monday/Tuesday prior to Thanksgiving. This year we are going just Sunday/Monday.
The park wasn't bad AT ALL. In fact, If I recall, Tuesday started getting busier than the other days. I think this may have been the trip that Miley was in the park on Sunday.....and we didn't even know it (we avoided the area in front of the castle when we saw the stage set up, didn't even know it was for her).
We prepared for the worst and were pleasantly surprised. So surprised, that, we are going back again that week this year.