The place that is going to be the first to celebrate new year's day on January 1, 2000 is going to be a place along the International Date Line, which runs through the Pacific ocean a little to the west (left) of Hawaii. Hawaii will therefore be one of the very last places to celebrate the new year. See How Time Works for information on time zones and the IDL.
The very first place is probably, technically, going to be in Antartica. Antartica will be experiencing nearly full daylight at that moment, and there is a location in Antartica that is exactly on the IDL. But it would be a really tough place to deliver your baby. So, ignoring Antartica, the place seems to be the eastern-most island of Kiribati, called Caroline Island. Kiribati is a nice Island country near French Polynesia, and this would be a very nice place to deliver a child compared to the the land of penguins!
If you want to learn more, here are several helpful links: