Isn't the USA 0 miles away from Hawaii? Strange that North Korea is closer than South Korea or Taiwan or the Philippines, I'll have to look at a globe maybe. Though I got everything other than the Cook Islands.
Or go to Google Maps. Right click on Honolulu and choose Measure Distance. Then click another spot on the map. You can drag and drop the end points around, or click one of them to disappear it.
The closest state in continental USA is Alaska, 3517 km/2186 mi north. Of the contiguous lower-48 states, Point Arena, CA is closest at 3678 km/2286 mi away, so if that was a separate country (which, until 1898, it was) it would rank 3rd.
Hi Glacier, Cook Islands and Niue are countries in free-association with NZ, much like Marshall Islands are in free association with the US. Try flying to those places, and you'll see what I mean: even New Zealanders have to depart for those places from the NZ international terminal, and must clear NZ customs. On arrival, you pass through Niue and the Cook Islands customs, and your passport gets stamped with a 30 day visiting permit with an "employment prohibited" endorsement. There's a weekly Air New Zealand direct flight between Los Angeles and the Cook Islands - come over for a week or two's holiday, and notice how your passport gets an entry stamp not to New Zealand, but to the Cook Islands. Cheers, Jeremy