Apart from Kindle where you can download a lot of books for free, I’ve found two websites where you can find picture books and other books for kids.
If you don’t have time to make it for the Story Time at your library, you can always find very nice stories online. Just click on a title and let someone else read the story to your child.
International Children’s Digital Library
Here you have to read the books yourself but it is a good resource if you travel and can’t take actual physical books with you. Read the directions how to find books in English (there are books in other languages there as well)
Librivox Free audiobooks, including children’s audiobooks.
Librophile Free e-book sand audiobooks, including children’s books.
Storynory Free audio-stories for kids.
Lit2Go Free ebooks with audio.
Open Culture 200 Free Kids Educational Resources: Video Lessons, Apps, Books, Websites & MoreSharing is good karma: