Dumpster diving near big stores are touch and go in my area. Alot of stores have reverted to compactors instead of traditional dumpsters.
That and most things are destroyed/not edible by the time I get to it.
I'd be on the lookout for community clean-ups (ie: large dumpsters that are in neighbourhoods for a week or so), construction sites, libraries, schools (especially universities near the end of the semester), plenty of places that are in or around a city.
And most dumpsters behind stores are not owned by the stores, but by companies who collect trash. They are the property of whoever owns the actual dumpster. Look for a sticker on the dumpster. It will probably tell you.
Keep in mind the law though.