Cannot find where Google Play Music stores downloaded files (different from similar posts)
In the settings of Google Play Music, if you have it set to cache on the external SD card, your cache location will be /external_sd/Android/data/com.google.android.music/files/music/.

If you have it use the internal storage, the path will be /sdcard/Android/data/com.google.android.music/files/music.

Note that these files are named [some-id].mp3, like 124.mp3. So just copying them from this location will be difficult to determine what song they are. Not only that, as GiantTree mentions, the files are encrypted, so even if you copy them off, you cannot play them. It requires Google Play Music to play them.

Here is a screenshot of my files on the external sdcard that I navigated to within droidexplorer. 



And Here is using Windows MTP to browse the files.