Every local farmers market I've been to has been less expensive than a grocery store. I literally come away with enough food for the week at half the cost of the grocery store produce (Safeway for me). Whole Foods? Probably 1/4th the cost.
Really, truly what I'm saying is true. For people who don't even have a grocery store, I think things like community gardens (a garden that is shared between a block of neighbors) is a perfectly scalable, healthy and affordable solution.