Public Libraries of West Virginia
Their postcards do exist, but not in large numbers. Service is organized at the county level.
Charleston
As this Acmegraph postcard was mailed in 1915, we can rule this building out as the 1934 Library. I believe it to be the Kanawha & McFarland location. As the 1934 building is also located here, I'm going to call this building demolished.
The current building could use some TLC, too.
Clarksburg
Affectionately named "Waldomore," this antebellum building is now part of a library complex.
This unusual postcard has no attribution.
Morgantown
This 1964, highly modified, is part of a city system.
The date comes from the reverse of the Lusterchrome postcard.
Weirton (Mary H. Weir Public Library)
From the Luoma Photos postcard:
Built in 1958, and given to the people of Weirton by Mr. & Mrs. R.T. Weir, the library promotes cultural and educational materials for Hancock & Brooke Counties. The Library houses approx. 50,000 volumes.
Even if the card hadn't given the date, you could peg it within 2-3 years. The building is still in use, with slight modifications.
Weston (Louis Bennett Public Library)
This former house was donated in 1922 for use as a library. It has served thusly since 1923.
Its NHRP nomination form calls it High Victorian Italianate. It's certainly a beauty, but I can't imagine navigating all those levels.
The postcard was made by the Tecraft Company of New Jersey.
Wheeling
In 1904, Wheeling voters, mainly coal miners, rejected a Carnegie grant to strike out on their own for a new library building. The image shown was the 1911 result.
By 1979, the Gilmer Public Library served the city: now a single system, the Ohio County Library, serves Wheeling. Nowhere along the way in the several history documents online does it state outright that this was demolished, but photos online bear no resemblance at all to the C.T. Photochrome postcard.