osmAnd allows you to use a number of different sources, though their business listings are inferior (in Los Angeles/San Diego) no matter what source you use (admittedly this might be partly due to new businesses opening, I've never tried searching for a long-established business as I already know where to find these). Recommend installing from fdroid, the play store version is limited (may not make a difference to you)
There's a number of other map apps around as well (Mapfactor, MapQuest, maps.me), including some for specific purposes (transit, Waze, Polaris, backcountry, sygic)