Whenever I listen to Google Music,I always leave it on shuffle and I forget about it. Often times I quit the window forgetting I have it open. If there was a dedicated app, this would not be a problem. Well, why can't we do a simple dedicated app, until Google releases a better one? Its actually quite easy.
1) Download Fluid from Fluid - Turn Your Favorite Web Apps into Real Mac Apps.
2) Set the settings to music.google.com and name it whatever you want( I named it Google Music)
OPTIONAL: Creating an icon
1) Download the Google Music icon from here: [link]
2) Save it somewhere convenient, like the Desktop
3) Go to iConvert: Convert ico, icns, and png icons online for Windows, Mac OS X, and Linux
4) Select the image and convert to the .icns file(the first one for mac)
5) In your newly created Google Music app, go to preferences>general
6) Click on the button to change your icon(its the lower most one)
7) FInd the new .icns in the downloads folder