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There appear to be a number of U.S. counties that consist entirely of islands:
 
In Hawaii there are Hawaii, Honolulu, and Kauai.  Maui County consists of a
number of whole islands and most of the island of Molokai; the remainder of
Molokai is the small county of Kalawao (a leper colony).
 
Massachusetts has Dukes County (Martha's Vineyard and the Elizabeth Is.) and
Nantucket (covering the island of the same name).
 
New York has New York County (Manhattan I.) and Richmond County (Staten I.)
 
In Washington the northwest corner of the state is San Juan County, all islands.
 
I think that is all there are.  A couple of other counties look a lot like
islands only, but I believe each has a land connection to the mainland or
takes in a bit of the main:  Island County in Washington and Grand Isle
County in Vermont
 
There were others in the past that are now gone.  The province of New York
had its Dukes County (1683-1691), which consisted of today's Massachusetts
islands of Nantucket, Martha's Vineyard, and the Elizabeths.  In the same
region, Rhode Island's Newport County covered only islands in Naragansett
Bay from 1703 to 1747, when it added some mainland on the east.  In the
nineteenth century Michigan had two counties composed of only islands:  Isle
Royale in Lake Superior stood alone as a county from 1875-1897, and from
1855 to 1895 the county of Manitou covered the islands in the north end of
Lake Michigan.
 
I pulled the historical information from our Atlas of Historical County
Boundaries, but the current information is easy to find in almost any modern
atlas or on a map of counties, such as the Census Bureau publishes.
 
In return I have a question.  What is your faculty member looking for?  What
is special about island counties?
 
John H. Long, Editor
Atlas of Historical County Boundaries
The Newberry Library
60 W. Walton St.
Chicago, IL  60610
Tel:  312-255-3602