I just got my new (used) bike, and I'm also a big music nerd and love to listen to music when I'm traveling. Do you personally listen to music while you're cycling, and in your opinion is it safe?
I listen to music or podcasts while cycling to/from work everyday, but at low enough volumes that I can easily hear traffic around/behind me. I would not recommend it if you've just started cycling, but if you're comfortable enough on a bike in city traffic it should be okay. Just make sure you're always constantly aware of what's happening around you.