So sometimes they played a show/concert with an artist I already like. Sometimes it just comes up in the YouTube feed. Sometimes somebody points me to something and it takes.
I took a few local venues that I like, and put the top song from each of their headliners for the next month into a spotify playlist, then just listened on shuffle while I was doing something else. Occasionally a song jumps out, and like that! I've discovered a new artist I like, and I can go to their upcoming show to boot!
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.
* Use the Shazam app on my phone to identify music I hear in public places
* Go on Rateyourmusic.com, look up an album I like and find what "lists" RYM users have put that album on, or what message board posts have cited that album. It's a much more "human-centric" approach compared to websites where algorithms generate the recs.
I attended a somewhat notable music festival this year and I noticed that the bands on the line-up had all the other bands from the same festival in the "similar" section, despite not being similar at all - (I'm assuming) just because other people interested in the festival were checking them out.
I use Google Play Music and when I find something I like, I buy the CD.