How about this: some phones have an FM receiver and most phones have bluetooth. Some phones stream music over bluetooth (called A2DP). I haven’t tried streaming FM from a phone, but it might work. It would be like streaming music to a bluetooth headset.
Also, if you have a smart phone you could listen to stations on the internet, through your phone, like I “heart” radio, Pandora, Slacker, etc. You could get some local stations that way, possibly your favorites.
It would take some research but it might be possible to stream FM radio on your phone to a bluetooth device. I had a Nokia 5310 with FM and my current phone, the My Touch 4G from T-Mobile (great phone and fast 4G Internet) has an FM radio but you must plug in headphones that act as the antenna (so no streaming of the FM output).