Lilliput. Brobdingnag. Laputa. The Land of the Houyhnhnms.
If you have an Amazonian island, you should also have an Athosian island for them to raid and where they send the male children. Consult your gay friends for suggestions for both.
An archpelago of halflings, one clan per island, with an elaborate kinship system in place of a government.
A gnome island, which started off as a boat.
An island at the bottom of a dimensional vortex, inhabited by people who have mysteriously disappeared from other places. Amelia Earhart, Benjamin Bathurst, Ambrose Bierce, Glen Miller, the Roanoke Colony, Judge Crater - they're all here. One of the island's primary resources is odd socks, and their currency is all in small change. This island is extremely difficult to sail away from - it keeps sucking you back.
Island of the Lotos Eaters.
Circe's Island.
Island of Polyphemos.