This place is super authentic - don't believe me, because I'm as European as they get - believe my Mexican husband from Palm Springs. According to him, this is exactly what Mexican supermarkets are like in Southern California. It makes him feel more at home since I made him move from the desert to Cleveland, where it's sunny, you know, 7 days a year.
Back to La Plaza: there's even a jewelry store in there! If you are looking for some sort of Mexican brand or ingredient, you will find it here. The prices for spices, etc is much more reasonable than if you were to buy it elsewhere. Their chorizo is incredible - flavorful and not as greasy as you find in normal supermarkets. On the weekends they have a taco cart in the store.