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Assuming you mean Hawai'i as a state and not Hawai'i as an island, there are several good candidates for the closest island.

Palmyra Atoll, an unorganized incorporated territory of the US, is about 1000 miles south of Hawai'i.

Johnston Atoll, an unincorporated territory of the US, is about 1400 miles west of Hawai'i.

Guam is located in Micronesia; it is NOT a part of the Northwest Hawaiian Islands. It is an organized, unincorporated territory of the US, located about 3800 miles northwest of Hawai'i.

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