The website Free Kids Books also provides free bedtime stories. It categorizes the stories according to different age groups, so it's easy to find something suitable for your child. You can find simple stories for younger kids and more complex ones for older children.
You can try websites like Storynory. It offers a wide variety of free bedtime stories for kids. There are classic fairy tales, original stories, and even stories with moral lessons.
Another great place is Librivox. It has a collection of free audiobooks which include many bedtime - friendly stories. Volunteers record these stories, and you can just listen to them for free before going to bed. It's a wonderful resource if you prefer to listen rather than read.