I don't know about you, but that's not how I listen to music. My idea of a great playlist is a mix of Zac Brown Band, Prince, Van Halen, Kenny Chesney and a some Rumpshaker. Sure, you can create a playlist that contains that music but with a playlist that I create I'm hearing the same songs over and over again. There's no discovery.
Sure, Google Play Music has the "Thumbs up" auto-playlist, but again, it's the same songs over and over again (plus any new ones I add). There's no discovery.
Google's "I'm Feeling Lucky" feature should be the answer to this need. But, for some inexplicable reason, Google Play Music's "I'm Feeling Lucky" feature produces a genre-specific playlist. That playlist will likely be very nicely tailored to your preferences if you use the app a lot. However, you're locked into listening to one genre at a time. Every time you initiate "I'm Feeling Lucky" it changes to another genre. I don't know the rationale for that design decision but it makes no sense to me.
Luckily, the Google Play Music webpage has a way to overcome this significant limitation in Google Play Music. If you've got a history of "thumbs upping" songs you like within Google Play Music then follow along. You'll like this. Open Google Play Music on the web (not the smartphone app). Click here. Make sure your current listening queue is completely empty before you continue.
In the upper left corner, click the three bar menu icon, then select Music Library.
Scroll down the page and find the section called Auto-Playlists. There, you'll find an Auto-Playlist called "Thumbs up" which represents every song you've ever thumbs upped in Google Play Music.
Now you have a new playlist called "Jeff's Mix" in your Playlists which, at the moment, is identical to your "Thumbs up" Auto-playlist. If you have several hundred songs in your thumbs up playlist wait for a few minutes before you proceed to the next step. If you proceed and get an error, wait a little longer.
You've just created a custom radio station, not based on a single genre or a particular activity, but rather based on your unique collection of thumbs upped songs. You'll find it in the radio station section of Google Play Music. Mine is called Jeff's Mix Radio.
You've just created your own personal radio station based on the songs you like, with the added benefit of music discovery! It won't take you very long in the listening experience of your new radio station to begin hearing discovered music that wasn't thumbs upped by you before. As you listen, you can thumbs up / down as you like to further tune your custom radio station. If you download offline on your smartphone, each iterative refresh will be tuned more and more to your liking.
It may seem silly to have both a Jeff's Mix playlist (static) and Jeff's Mix Radio (dynamic with discovery) but I'd recommend not deleting the static playlist. I've noticed that if I delete the static playlist that the radio station ends up disappearing as well.
It's a shame that Google can't just give us a straight forward way to enjoy multi-genre music discovery but until they do this is next best option. Enjoy!