
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.
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I have no history on this rather more permanent-looking structure, but it appears to have been replaced by the building below.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.
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.