It is hard to say, because the Earth is constantly in move. It also depends on the part of the year. However, they are the countries near an international time line that see a sunsets first: Fiji, New Zealand, Japan.
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The answer to this question could be tricky. Since the earth is constantly rotating, it is hard to mention a country where the sun rises the earliest on a day. 'A Day' is just a man-made phenomenon. 'The international Date Line' is the line which separates the world. It is the line where a calendar day begins. With respect to this line, the republic of Kiribati is the first nation to see the first sunrise of any day.