Our son E loves to read but it is hard to keep him in books. We brought some with us, but those went fast. So we had to find new ones. We live close to the central library, which is good for rainy days too. They have English versions of the Harry Potter books and selections from the classics: Treasure Island, Arabian Nights, King Arthur and oddly, Roald Dahl's BFG. They can also order other English books from other branches. There are also several bookstores that have good English selections. Junkudo in BAL on Kawaramachi just south of Sanjo has perhaps the best selection, but the other big stores have several English books as well. We have also been to the bookstore in Aeon Mall south of the station. As always Amazon is a good option too. We got some good "One Piece" mangas via Amazon.
There are some used choices as well-the YWCA (west of the palace) has a book exchange that has some young adult books. We've also trawled Green eBooks (on Marutamachi east of the Kamogawa) for the few young adult novels they had. Their inventory changes and they might have more on other occasions.
Finally a good option is to exchange among friends. We do this with our friends and it multiplies the number of books each of us have.