If you are determined to have an automated method, you can find neighbors using this approach.
Then look for counties with no neighbors. For these counties look for the closest counties in the same state and add these to the list. 

But that seems like a lot of work for a small problem. A cursory search suggests the number of island counties is quite small and you can patch up the data by hand:

1. Hawaii (All 5 Counties)

As the only state located entirely on an archipelago, all its counties are island-based.

  • Hawaii County: The "Big Island."

  • Honolulu County: Oahu and the Northwestern Hawaiian Islands.

  • Kalawao County: A small peninsula on Molokai (the smallest county in the US).

  • Kauai County: Kauai, Niihau, and others.

  • Maui County: Maui, Lanai, Molokai, and Kahoolawe.

2. Washington (2 Counties)

While most of Washington is on the mainland, its northwestern corner is home to:

  • Island County: Comprised primarily of Whidbey and Camano Islands.

  • San Juan County: Comprised of the 170+ islands that make up the San Juan archipelago.

3. Massachusetts (2 Counties)

  • Nantucket County: Coextensive with Nantucket Island and its tiny neighbors (Tuckernuck and Muskeget).

  • Dukes County: Comprised of Martha's Vineyard and the Elizabeth Islands.

4. New York (2 Counties)

Technically, two of New York City's boroughs are their own island counties:

  • Richmond County (Staten Island): Comprised of Staten Island and surrounding smaller islets.

  • New York County (Manhattan): Comprised of Manhattan Island, Roosevelt Island, and others. (Note: A tiny 0.1 sq mile neighborhood called Marble Hill is physically on the mainland due to a canal being dug in 1895, but it remains legally part of the island county).

5. Rhode Island (1 County)

  • Newport County: While some of its towns are on the mainland, the county itself is largely defined by Aquidneck Island, Conanicut Island, and Prudence Island. However, it is often excluded from "entirely island" lists because a portion of the county (the town of Little Compton and Tiverton) is physically attached to the Massachusetts mainland.

6. Florida (1 County*)

  • Monroe County: This is a "hybrid" case. While the populated Florida Keys are entirely islands, the county boundaries actually extend onto the mainland to include a large, uninhabited portion of the Everglades.


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