What are the two closest capital cities in different time zones in order to celebrate New Year's Day in both capital cities?
Well this is an easy one to answer if you ask the right question!
"What is the only capital city with 2 different time zones"?
You can celebrate New Year twice in Nicosia (capital of Cyprus), once in each half of the city!
Nicosia now holds two distinctions. It is the last divided capital in Europe after the fall of the Berlin Wall — a United Nations buffer zone separates the Greek southern part of Cyprus from the Turkish-Cypriots in the north — and it is also the only world capital that follows two time zones.
And no one is quite sure what to do on New Year's Eve.
Michalis and Tanur say if they can make their mixed marriage work, the politicians should be able to mend fences between the two communities.
The couple is organizing two street parties on New Year’s Eve to celebrate but also to protest the time difference. After midnight in the north, they plan to pass through the buffer-zone and celebrate the New Year again in the south.
Of course, everyone can just wait for spring and the return of Daylight Savings Time, when all Cypriots will be back on one time zone.
While these aren't quite the closest, they potentially give a decent amount of time to get from one to the other and still celebrate New Years in both:
Apia, Samoa (UTC +14) and Rarotonga, Cook Islands (UTC -10). Distance between the two is 1500km, however you'd probably need to charter a flight as there don't appear to be direct flights between the two. There are flights via Auckland, New Zealand
Or much much closer, although one isn't technically a capital city:
Speaking of capitals, Minsk (Belarus) and Vilnius (Lithuania) seem to be the closest. Minks is in UTC+3, Vilnius is in UTC+2. There are approximately 170 km between them. It would be hard to travel this distance in less than one hour.
The next closest pair would be Seoul and Pyongyang (South and North Korea). There are about 200 km distance and 30 (!) minutes time difference (UTC+9 and UTC+8:30).