We went for the Millennium (Dec. 31, 1999- Jan. 7 2000). While New Years Eve was like trying to walk through a sardine can (Epcot), it was FANTASTIC!!! It will be crowded the days leading up to New Years, but we found the morning of New Years Day to be wonderfully empty at the parks. By the 2nd, no one was around! I would think the day of the week would make a difference. Since NYE is in the middle of the week this year, I would think the crowds would stay around through Saturday.