I have given up on music on the radio. I have not heard good music on the radio in years. Instead, I listen to talk radio and podcasts. And my favorite topic for either of these is the food talk show. Food talk radio is the best radio that you will ever hear, and you will not want to listen to another type of radio ever again.
Unfortunately there is not a single radio station that has 24 hour broadcasting of various food talk shows, such as Raw Food Talk, Apples and Oranges, or Sushi for You and Me. I just made those up, but I would absolutely listen to every single one of them happily. But, you do have a few options for hearing a constant stream of food radio, so you should certainly look into one of them.
Your first stop should be to see the schedule of your local public radio channel. Very often public radio will broadcast food radio shows at set times every week, even if you are in New York and the show comes from California. Public radio stations know that people love food, so they will play these shows, as it is what the listeners want to hear.
If you are not available to hear the shows when they are played, or you just want to listen to them on your own time, you have two more options. You can go to the site for each show and listen to their latest broadcasts there, right through your browser. Or, the technique that I use, get their podcasts. You can listen to them whenever, wherever, right through your phone. And any phone will have a podcast app that you can use to make it easier.
Podcasts of note, that I highly recommend, are Good Food from KCRW, Americas Test Kitchen, the Splendid Table, and the BBC Food Programme. All are exceptional in their information, and all are very different in content and delivery. You can listen to all of them, one right after the other, every week, and never hear the same stories or get bored. Stop starving your brain while stuffing your stomach. Nurture both with good food content.