Many people have now included "music player" with the other things they have delegated to their phones to do. I've tried this, but it's not for me. My phone is a busy little thing, and all those boops and bings and bongs it emits mean something. Such interruptions don't mix well for me with a stream of music being played, which I treat as a form of meditation.
So when yet another MP3 player went on the fritz, I took a different path. Based on a tip I read online, I searched on eBay for an Android phone with a bad ESN. A phone with a bad ESN is a phone that can't be activated on a carrier: but that makes it sell for under $20 -- even under $10 for some.
I ended up with an LG MS870, which runs Android Ice Cream Sandwich. I rooted it, to eject the bloatware. I connected it to my WiFi - so I could even make calls on it if I wanted to, using Skype. I downloaded the classic Winamp Android app from the Winamp Enthusiasts site. I paired a nice Plantronics stereo Bluetooth headset to it... et voilà! A dedicated MP3 player for under $20 that won't interrupt the play with anything mundane.