Grand Isle County, Vermont. Several connected islands. Any others?
In Washington State, there is Island County.
The county’s name reflects the fact that it is composed entirely of islands. It contains two large islands, Whidbey and Camano, and seven smaller islands (Baby, Ben Ure, Deception, Kalamut, Minor, Smith, and Strawberry).
Manhattan(New York County) and Staten Island( Richmond County).
Hawaii? Four counties. Or is that cheating?
The town of New Shoreham is entirely comprised of the actual island Block Island, in the state of Rhode Island which is not an island. New Shoreham is part of Washington County, which also comprises most of the mainland area known as South County, which has no legal existence, but is the summer vacation destination of much of New England.
[Damn - I caught myself waiting for my fellow Rho Dislander Tripolar to mention this. Miss that doper!]
Nantucket County and Dukes County (Martha’s Vineyard and surrounding islands) in Massachusetts should qualify.
Not sure if this is what the OP is looking for, but Long Island in New York contains four counties - Kings, Queens, Nassau and Suffolk.
And I have to nitpick on the earlier mention of New York county - there’s a tiny bit on the mainland, the neighborhood of Marble Hill which is surrounded by the Bronx on three sides and the Harlem River on the south, is part of New York county, as well as all of Manhattan island and a few other surrounding islands.
Isle of Wight, UK
If you want to include Alaska’s census areas and boroughs, there are a few others - Aleutians West and Kodiak for sure, possibly Sitka
San Juan county in Washington state should also count (the San Juan Islands).
And San Juan County.
San Juan County comprises San Juan Island, Orcas Island, Lopez Island, Shaw Island, Blakely Island, Crane Island, and Decatur Island.
Good point!
Island County came to mind first because, well, it’s literally “Island County”.
Perhaps surprisingly, the Florida Keys are not a county of their own. They’re a section within Monroe County; a county that has vastly more mainland area than island area. But all of Monroe County’s mainland area is uninhabited Everglades swamp / nature preserve.
So from the population’s perspective, it’s an all-island county that was given a big block of mainland nature preserve / swamp to manage also. The county seat is in fact Key West out on the tippy end of the island chain.
It surely doesn’t fit the OP’s definition strictly, but maybe gets an honorable mention or an asterisk by its name.
The northern most part of the county (Alburgh and Rouses Point) aren’t an island, they’re attached to the Canadian mainland.
Dare County NC is mostly islands (the Outer Banks) but also includes a big chunk on the mainland.
Some of the Louisiana Parishes south of New Orleans are mostly islands and swamp, but some of each is part of the mainland.
Aleutians West - Yes
Aleutians East - No
Kodiak - No (a big chunk is on the mainland)
Sitka - Yes
Hoonah-Angoon - No
Prince of Wales-Hyder - Yes
There are a number of Australian instances of LGAs (local government area), our equivalent of a US county, which are islands including:
Cocos (Keeling) Islands
Christmas Island
Lord Howe Island
Kangaroo Island
King Island
Norfolk Island
Groote Eylandt
Rottnest Island is not an LGA
Gawd knows how many instances there are on Indonesia.