Libraries are usually picky about donations. I had to weed my personal library when we moved from Palm Harbor, FL to the Villages in 2005. Donated many books to the Tarpon Springs, Oldsmar, and Safety Harbor Public Libraries but there were many books no library wanted. Law text books, other text books, various older novels of lesser writers, etc. Had to throw a lot of these in the trash.
I had sold my best art books and other prize items from my library to a Santa Rosa, CA used book store back when we moved to FL in 1996 from Northern California. I also had needed the money to send stuff out to people via the mail in the 1990s.
Try the area used book stores if you have books that might be in high demand like very nice art books, first editions in good condition, etc. You might also Google online used book buyers.
I did find this but have never used them--
Sell Your Books and Sell Back Textbooks At sellbackyourBook.com