My definition of "grocery store" requires that they sell fresh meats, fruit/vegetables, and bread other than Wonder-type. No 7-11 type convenience stores. Walking distance? If you can walk there in 10-15 minutes, that qualifies.
I currently live walking distance from a full line, albeit very small, store. (Detroit MI suburb)
I know this is going to be different for region/country so please specify city/state and country if outside the US.