Hi,
You can try the smaller Arizona supermarkets. They have less choice. They carry your common household brands but it is usually a bit less expensive.
For fruit and veg, I heard there are some green grocers that are fairly better priced than the numea market.
Keep your eyes peeled as you drive around because there are quite a few people growing their how veg who will put up a sign saying what they sell.
Other than that life is expensive in New Cal no matter what.
But as you get to know more and more people you will find out that people will gladly give exchange whatever they grow in the garden, the fish they caught or the game they have hunting so it doesn't go to waste.