"several hundred" is really not very many books, says the person with over a thousand. :-) If the LW's dad lives in or near a university town, the first thing to try is a departmental, alumni, or university-library book sale or swap. Books collected by an academic are typically of interest only to other academics.
A small-town library typically will only be able to use good-quality hardcover copies of popular fiction or literature titles that will get circulated a lot. But they may indeed be eager to have the collection for a fundraiser sale.
As to where the father should start with downsizing ... a shelf a day. He can just look at one shelf, flip through each book, decide if he can let it go now versus later.
After 20 years, I found it very easy to get rid of my academic collection, whereas only 10 years out it was hard to let go. He may be ready.
