Sort books. Maybe some of them still take to the library. Call and find out literature what subjects are in demand. Modern library gradually ceases to be a place where you just keep on time and borrow books. It is more like a social club, where the collected literature on a particular topic, conduct meetings, lectures and literary salons. It is possible that you have literature on local history, the history of technology, art, which may be of interest to readers. By the way, is now actively creates private libraries. Their owners collect the literature on a chronological or territorial basis, and sometimes even looking for books that were once sold to the load.
Antique books will be in a used bookstore. The number of such stores in recent years, of course, greatly reduced, but in big cities they are still there. Find out what books are in demand. For they could be sold for a certain amount, sometimes very solid. To a used bookstore you can take and not very popular books, but they will be giving away, most likely for free.
Children's books can be attributed to the nearest kindergarten. Preschoolers have not yet switched to e-reader, they still need regular picture books. So your selection may well find a place in the methodical Cabinet or even in the book corner, one of the groups. Such books will be there and the orphanage.
Fiction and non-fiction literature you can take home for the disabled or elderly. The older generation used to read, besides they are not too actively exploring electronic devices, so would be grateful for the gift. By the way, if there is a nearby resort or rehabilitation centre with non-stop stay for the elderly, there also may be interested in your offer.
Sometimes even people who have mastered the computer and e-reader, I prefer regular books. In social networks there are many communities where users are offered something to give away or to sell, including books. Such groups are in the "Live Journal", in "Vkontakte", "Facebook". Make a list of the books and write the post that you want them to give away or sell for a small price. Do not forget to specify the city. Those interested will certainly find. By the way, if you don't find any such community in your social network, create it yourself.
Advertise that you give your library, on the website "Botrivier". There need to register, but it is quite simple. You can write a message and on your city forum.