Let’s face it, most free apps suck for offline music. Trying to find gold in a heap of rust. But okay, I’ll humor you. Your best bet is Spotify’s free tier allowing for some offline playlists. They like to keep you on a data leash but you can download a few songs at least.
Other than that, try Evermusic. You can upload your music from cloud storage to the app and play it offline. Some people rave about it like it’s the second coming. I’d say give it a shot.
Lastly, there’s VLC Media Player. Import your own music and store it offline. Sure, it’s not a buzzy music app, but it works. So unless you want to pay, these are your best options. Don’t expect miracles.
Hope that helps, sort of.