Naive as I am (& not living in the US), I've always thought these supermarket chains have uniform pricing and that's one reason why they're so popular.
Living in Canada, this is rarely the case (probably because it's too cold here to grow... most things.) Here in Vancouver, our strawberries comes up the coast from California; our lettuce tends to come all the way from Mexico; etc.
But milk and dairy and eggs are often packaged relatively close; but you might not know it unless you know how to read the packaging codes.