
Public Libraries of Alaska & Hawaii
Alaska
Anchorage

I believe this building is still in use, heavily remodeled, as the Anchorage Municipal Library. How the Library differs from the Z. J. Loussac Library, I'm uncertain.
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The photo postcard is labeled as an Alaskan Post Card, via rubber stamp. The cars seem to date it to the mid-1950s, which would be during territorial days.
Fairbanks

Photo by Cann's.
A reading room predated this building, the George C. Thomas :Library. As one might expect, it burned (1942).
Juneau
Memorial Library
T. Davis photo.
I have no history on this rather more permanent-looking structure, but it appears to have been replaced by the building below.

Here, the Library has been combined with a parking garage. I have only seen the like in Madison, where the University's Helen C. White Library also sits atop parking.
This postcard was produced by Mitchell Color Cards.

Nome

Sometimes a street scene, with the Library on the left, is the best that can be done.
I don't think that this is the Kegoayah Kozga Library. Its website provides a thoughtful tour of the interior only.
Hawaii
Both the single Carnegie library and the rest of the 50th state's libraries are included in a single section. Would you be choosing library postcards on your Hawai'i vacation?
(I would be. No kidding.)
Honolulu (Library of Hawaii)

Designed by Henry D. Whitfield. A partial Carnegie grant was made in 1911. Other US territories with Carnegie libraries were Arizona Territory and Indian Territory.
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The postcard was printed by E.C. Kropp for the Island Curio Co.
Lahaina

According to the H.S. Crockett card, this library was built in 1955.