We spent the (very long) day in Epcot on NYE 2000/1.
We'd heard stories of the parks being at capacity early on, so we were through the gates by 7:15 a.m. Yes, that's 7:15 in the morning!

We stayed until after the midnight edition of Illuminations and it was a fantastic day. We were completely exhausted, but I would happily do the same again if we had the opportunity.
One of the most frustrating things I found was the lack of advance information about park operating hours, etc. I was able to confirm opening times for the parks only the day before NYE. There were two showings of Illuminations, with an earlier (unpublicised) version at about 7 pm, then the NYE version at 11:45 pm.
We liked Epcot because there were mini celebrations in each of the World Showcase pavilions as their home countries reached midnight - we booked a PS in the Rose & Crown to be there for 7 pm when it would be nidnight back home.
There were stations around the park giving out hooters and hats during the evening, and stages set up with music playing throughout the evening.
In a word - brilliant! I hope you have as good a time as we did
