Keep text in TextView with drawableLeft centered

Though fragile, you can avoid the use of a wrapper Layout by setting a negative padding on the drawable:

<TextView
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    android:layout_centerHorizontal="true"
    android:drawableLeft="@drawable/icon"
    android:drawablePadding="-20sp"
    android:text="blah blah blah" />

You'll have to adjust the padding to the width of the drawable, but you're left with just a single TextView instead of an extra LinearLayout or etc.

You can set the parent of the TextView as a RelativeLayout whose width is match_parent.

<RelativeLayout
    android:layout_width="match_parent"
    android:layout_height="match_parent">

<TextView
        android:id="@+id/edit_location_text_view"
        android:layout_width="wrap_content"
        android:layout_height="wrap_content"
        android:layout_above="@id/add_location_text_view"
        android:gravity="start|center_vertical"
        android:layout_centerHorizontal="true"
        android:drawableStart="@android:drawable/ic_menu_edit"
        android:text="Edit Location" />

</RelativeLayout>