Is there any country that doesn't celebrate the New Year?

There has been no report that a certain country does not celebrate the New Year. However, different countries celebrate New Year on different dates based on the calendar they follow.

Countries like Russia, Ukraine, Belarus, Macedonia, and Bulgaria celebrate their new year on the 14th of January, according to the orthodox calendar they follow.

China celebrates its new year in the 12th month of the lunar calendar; the New Year date can fall any time of the year.

The Iranian New Year is known as the Persian New Year or Nowruz. It is widely celebrated as a holy day for Zoroastrians, Bahais, and some Muslim communities.

The Ethiopian calendar is a solar calendar, and the Ethiopian New Year falls on 11 September. There are more countries that do not celebrate their new year on the 1st of January.

There is no report that states that a certain country doesn’t celebrate New Year, but it is know that many countries have different dates for the celebration.

China celebrates the New Year around February every year.
Orthodox countries like Russia, Serbia, Ukraine, Belarus, Bulgaria and Macedonia celebrate the New Year on the 14th of January.

Iranian New year (Nowruz) is celebrated on the 20th of March
Ethiopia celebrates the New Year on the 11th of September; the country follows the Gregorian calendar.

Balinese and Javanese celebrates theirs around March, they follow the Saka calendar.
There are many other countries that do not celebrate the New Year on the 1st of January as many countries do.