I encountered a similar issue at 10.2.0: I had a MapView defined in XML like this:
<com.esri.android.map.MapView
android:id="@+id/map"
android:layout_width="fill_parent"
android:layout_height="fill_parent"
mapoptions.MapType="Streets"
mapoptions.ZoomLevel="3"
mapoptions.center="39.774769, -96.064453" />
When I ran the app, the Streets basemap did not display, just a grid. On pan or zoom, the basemap appeared as expected. I was able to work around the issue by changing "fill_parent" to "match_parent" for both the MapView layout's width and height:
<com.esri.android.map.MapView
android:id="@+id/map"
android:layout_width="match_parent"
android:layout_height="match_parent"
mapoptions.MapType="Streets"
mapoptions.ZoomLevel="3"
mapoptions.center="39.774769, -96.064453" />