I lived in Aptos, CA when the Loma Prieta earthquake happened. My home was about 10 miles from the epicenter.
My home came through it okay. Our cats were pretty freaked out but I don't think we even had any broken windows. (I've heard that the waves increase in amplitude as they get further away from the epicenter, so perhaps we were lucky to be so close.)
We were without power. I think phones were down but I'm not sure.
We didn't have much else to do, so we spent a lot of time listening to the radio. We learned some useful stuff:
* stay at home; the roads should be clear for emergency services.
* Cook and eat the contents of your freezer and fridge before things go bad.
* don't drink the water without boiling it, but it's okay to flush toilets.
* (Later) Okay, the water lines tested out, so go ahead and drink the water.
Also, we heard updates about the freeway bridge that collapsed, the destroyed buildings in San Francisco, etc.
But for the most part, the people talking on the radio didn't have anything too important to say. They filled a lot of airtime with repetitions of the above points, comments like "oh this is terrible", etc. So we stopped listening after a while and read books.
Still, in any future emergency, I will want a radio. The Internet could be down but the radio will still work. Lower-tech old-fashioned solutions are great in an emergency.
Just get a low-tech radio, rather than relying on a radio feature in something complex like a smartphone. Bonus points if you have solar cells and/or a crank to power the radio.