I think Japan and Taiwan are each others 2nd closest countries (check Yonaguni Island; it's a part of Okinawa Prefecture near Taiwan - that's in a proper province of Japan, not some offshore territory). Also, by my reckoning, Vanuatu is closest to New Zealand, with Fiji slightly closer than Tonga in second place.
For New Zealand, the closest is between Adams Island and Macquarie Island of Australia (621 km). Macquarie Island, although very far from the Australian mainland, is considered part of the state of Tasmania (unlike Norfolk Island which is self-governed). The second closest from New Zealand is between Raoul Island in the north, and the Minerva Reefs (624 km), which was annexed by Tonga in 1972.
Cool, thanks for that info. Distances between uninhabited offshore islands like these ones can sometimes trip me up! Your whole 2 Closest series of quizzes is great fun.