Most any modern cell phone can play mp3's as well as several other compressed and non compressed formats as well so you may not even need to buy a dedicated player.
Are you playing mp3's through the ipod or songs you have bought though itunes which are actually mp4. Despite Apples great fanism mp4 and ipod sound quality is pretty bad when played through anything but small headphones.
I'm going to order an aux in adapter for the radio in my truck because my phone can play mp3's at better quality than the cassette adapter I'm using at the moment.