I think your are looking for https://microg.org, an open and free replace for Google Mobile Services.
It provides free alternatives for maps and network location: replaces GMaps with OpenStreetMap and Google network location with the provider you want (I use Mozilla’s).
Plus, and optionally, it can connect to Google servers for GCM push notifications and Google device register. Note that this features can leak information to Google.
Of course, it removes the irritating “Google Services are needed”-kind of messages,
Just download the APKs (GsmCore, GsfProxy and FakeStore/BlankStore are the minimum) from the official site (there’s a F-Droid dedicated repo, too), install the below Xposed Modules and reboot:
- FakeGApps: http://repo.xposed.info/module/com.thermatk.android.xf.fakegapps
- XposedGmsCoreUnifiedNIp: http://repo.xposed.info/module/be.r3w6.intika.xposedunifiednlp
Edit: I wrote a post explaining Google Mobile Services and how they are putting AOSP in a cage. There you have: