Disclaimer: I don't know of any actual research, so this is an educated guess.
Video playback is the biggest draw of power for the nano; the battery only lasts for four hours of video compared to 24 hours for music. The CPU is constantly decoding a dense video data stream and sending it to the screen, which must remain on and backlit.
Since the radio's "data" stream is relatively light (no more than regular music) and the screen and backlight can safely turn itself off, I would say you could get rather close to the 24 rated hours for music playback. Perhaps a little less, as you'll want to change the station during the inevitable commercial break, which of course turns on the screen.
EDIT: If you're that worried about battery life, then get a USB car charger. They're cheap, universal, and handy. And if you dad already has his cell phone charging, no worry: there are multi-outlet adapters for cars, too. Then again, you may need a USB extension cord to reach your seat, if there are none besides the front console.
Color choice is totally up to you, and quite frankly, you can't go wrong; they're all attractive.
