You can integrate OSM by using the Osmdroid API. This gives you functionality very similar to Google maps but you can also use OSM tiles offline if you prepare the tiles with Mobile Atlas Creator (MOBAC)
See Osmdroid home page (GitHub)
You just need the osmdroid-android-3.0.5.jar in your build path. You don't need an API key like Google demands and tiles get cached, so next time you visit that location you save on data download costs/time.
It's got a few tiny bugs, but overall it's pretty good
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