If you sync to Google Music (Play) online then when you go to the music app do the following (make sure you do this on Wi-fi):
On the top left choose make sure you choose 'All Music' and not 'On Device Only'
Next go to the menu and select "choose on device music". Next to each album you want to keep on your device click on the pin. On the bottom you can see how much storage space you are using. After you choose your selections click done on top.
Go back to the top left and choose the option for 'On Device Only'
It will take a while but the albums will be downloaded to your device and you will only see in the app what is stored on the device so you won't use data. You can also choose playlists to download, so if you set up online a playlist that you want available you can have it available. I have a lot of albums online and don't want them taking up all the space on my device and in a lot of the albums I only care about a few songs, so I add them to a playlist and download the playlist which quickly gives me my favorite songs.