Web-based players are fine, but there are times when I'd prefer to have a native application for Google Play Music, for any number of reasons. Maybe I've already got 60 tabs open, and one more will drive me over the edge. Maybe I want to be able to use the play-pause controls on my keyboard.
So, I'm using Radiant Player for Google Play Music on my Macs.
First things first: This is not a native Google Play Music app for OSX. It's a wrapper for the GP Music website, basically. (If you've used Mailplane for Gmail, then you're used to this sort of thing.) This isn't an official app from Google or anything, but it's really good. And it has a couple tricks up its sleeve.
First is that it ties into your OSX notifications quite nicely. So if you're the kind of person who just has to be notified that way, have at it. It'll put a mini player in your OSX menu bar if you're looking for something else to take up a spot there, too. It's got a few options for skins as well. And if you're a Last.fm user, it'll tie into that, too.
For me, it was all about being able to use the play controls on my keyboard, and I don't mind the idea of offloading work from Chrome, too.
Radiant Player is free. You can download a fully working app, or dive into the code on Github. Get links to both here.