Kiribati is generally the first country to celebrate New Year's Eve each year because its Line Islands use UTC+14.
The Republic of Kiribati stretches across a large area of the central Pacific Ocean. In 1995, the country adjusted the date line around its eastern islands so that its territory would share the same calendar date. Kiritimati, also called Christmas Island, is the best-known inhabited island in the UTC+14 zone.
This answer depends on how “first country” is defined. It refers to the earliest national territory to reach January 1 under standard civil time, not necessarily the first inhabited place in every geographic or astronomical sense. Time-zone rules and daylight-saving changes can also affect comparisons among nearby Pacific countries.
Kiribati is not the same country as Christmas Island in the Indian Ocean, which is an Australian territory. Kiritimati belongs to Kiribati and is the Pacific island relevant to this New Year distinction.