There's an fdroid repo[1] for it, but I'm not sure I trust the person running it. Because of the lovely conversations with moxie the main fdroid repo got taken down. Don't you just love free software projects that hate giving users freedom.
That is a really good point, I actually got someone else to get it from the play store then copied it, the updates from apkmirror are then fine since the signatures match. I'll edit the post to say, get it from a trusted source.
This is also useful: http://www.onyxbits.de/raccoon
It's a dektop play store client.
I tried it out a while back and it worked, don't know about now.
Edit: The series is a little out of date, but should give you the general idea. ROMs that are probably new since that article was published that have no google dependencies are Replicant (entirely libre), OmniROM, Copperhead OS, and CyanagenMod w/ a no-gapps-script.