One might be able to make some good comparisons about rent, since that's so heavily market-driven... but groceries? I find that the price of groceries varies so widely across any city, or hell, any neighborhood that one cannot possibly make a reasonable claim to "a bottle of beer costs $X", nor "a delivered pizza costs $Y".
Take where I'm right now for example - your link has the broad area "Seattle-Bellevue-Everett" - which covers every single neighborhood in Seattle, from the cheapest in the Central District all the way to the most expensive in Belltown. And then it moves north to heavily blue-collar areas like Everett and software-engineer-land like Bellevue.
How can any reasonable pricing index be established like that?