Corner stores are rare even in the very urban part of town I'm in (Lakewood) and typically sell primarily booze, cigarettes, snacks, and lottery tickets, not anything that a person hoping to live another decade would actually want to consume.
Big-box, warehouse type stores like Costco offer better and fresher produce options, but require very long drives out into the suburbs and are typically at least as congested (both the stores themselves and the shopping centers they're in) as grocery stores in the inner suburbs.
Poor inner-city neighborhoods have even fewer options than the ostensibly middle-class areas like mine - sometimes, unless one can borrow a car or take 2 buses that run at best hourly, none whatsoever.
In short, trying to find decent food is a nearly unbearable ordeal here compared to most other places I've been, even within the U.S., and that probably goes a long way toward explaining why we're among the fattest and least healthy cities in a country not particularly known for leanness nor for good health to begin with.
Measure twice, cut once.