You're lucky! In my area, there are no such stations. All of the stations are essentially top 40 (in each of the major genres -- top 40 country, top 40 pop, etc.), talk, and sports.
There's nothing in any of those for me.
There are big names like iHeartRadio and SlackerRadio but lots of smaller radio stations have internet streams and/or apps. Podcasts are nice because they can focus on niche genres or provide more information about artists/releases. Mixcloud is one of my favorite sites for listening to radio shows.
It's a problem that I've solved long ago, really. Internet streaming services bring their own set of problems, so I don't use them.
I do listen to podcasts (downloaded, not streamed), but not for music.
I can advice you to listen to fip, it's a french radio with every genre of music.