My local public library has monthly used book sales run by the Friends association. Donated books and books culled from the library shelves go there, first. Some books, like duplicates of religious books get donated to the local outreach ministry. Some books will be moved on the the VA - they like westerns, thrillers and political books. A few times a year the Friends will have a $5/bag sale. And for those that no one really wants - things like 10-year-old copies of Books In Print, Old math & science journals and books in poor condition (that ratty 40-year-old Daniel Steele) are put on a free shelf outside the library book store and someone eventually takes them.
Something like your topic might find the best audience at a military hospital/retirement home.
While a nursing home, hospital, etc., might have a few patients who were really into Cold War history, I suspect that an extensive collection of books on this subject would be of limited value to such institutions.
That said, during a period when I was having daily radiation treatments at the hospital I was disappointed that the shelf of donated books in the waiting room had nothing but Harlequin type romances and a few Westerns. I’m sure I wasn’t the only patient who would have appreciated a little more variety – but the key word there is variety.
Back in the day, one room of our old Engineering School Library had a small collection of non-engineering books. Donated by some old graduate, just so that engineering students would have something to read, and to remind them that there is more to engineering than just textbooks.
The student union had a much bigger collection for the same reason, that was once a personal library.
Jails and prisons are VERY picky about what they will take. Not just for content, but how they’re bound; hardcover books are usually banned because they can be used to hide contraband or made into weapons.
How about an airport or train station? Some of them, especially the smaller ones, have their version of a Little Free Library and might be able to use them.
If you have some books that you know are of value (rare editions, signed editions), keep them together and clearly marked so they don’t just get boxed up and given to Goodwill. A large number of the others will be considered worthless if they have broken backs, torn or marked pages etc. You can donate some to nursing homes, or senior living residences. Consider who else would appreciate your particular books to help make sure they fall into the correct hands.
This thread reminds me that I have a rare copy to try to sell. Last I checked, someone was asking $120 for it, unsigned. I think I paid $7 and got a signed one. Time to check again.
Your book’s value is primarily the recycle value of the paper. There are plenty of libraries full of multiple copies of your book, you need not worry about the literary loss to society.