As I understand it, produce can be sold cheaper and better quality in local stores because it tends to produced locally, and local supplier eliminates the overhead that a big chain has. What is more, ethnic stores (Russian, Polish, Spanish, Asian, etc.) have their own distributors who import food items from overseas cheap. So what you have is a mom-and-pop store with low operating cost (low overhead), buying stuff locally or via their own distributor networks at low prices. However, they tend to operate in rather narrow market niches, mainly ethnic communities.
Manufactured goods is a different story because they are seldom manufactured locally - so to offer low prices you have to either lower your per-item transaction costs through the economies of scale (as large chains do), or have access to direct importers of cheap foreign goods (e.g. Chinatown stores). Otherwise, the only way to compete with large chains is to cut your own profit margin.
Another aspect is the transaction cost, or perceive transaction cost of shopping. As Chuck0 aptly points out, your average US consumer prefers what he/she is familiar with (i.e. local malls and supermarkets) and will seldom venture into unfamiliar territory of small shops, often located in urban areas, even if he could get a better price there.
Contrary to the conventional economic wisdom, US consumer is not a utility maximizer (e.g. looking for the maximum goods for minimum price), but transaction cost minimizer (e.g. looking for stuff that easiest to find. Consequently. Most middle class US-ers prefer malls and supermarkets because of their shopping convenience and do not look for bargains in unfamiliar and strange places.
Wojtek