A few years back I was in to audio books when I was waiting to get my cataracts done.
I have a reasonable selection of books from Audible that I use with their app, I have just given them a dustoff and started to listen to them again. I also have a selection of audio books that I downloaded from Bundy Library.
These come in mp3 format and I think I played them through either WinZip ooopsie WinAmp or VLC at the time. Had a quick look on the Playstore and come up with this one called Audiobook Player.
It's free of adverts, and will also play most file formats including Apple's audiobook format, have not tried Audible's in it.
In another thread I mentioned the Caroline Flashback app which is a paid app, and streams music.
However it does not have built in sleep timer, I found this one called Sleep Timer (Turn Music Off) which contains adverts. However it has in app purchases to get rid of them. I paid the price of a doughnut (less than $2.00) to the developer, which also includes a widget thingy and a cleaner look to it.