One of my favorite places to grocery shop is not even a place I can physically go to - it is Amazon. That has always been a favorite place of mine to shop and find good deals on toys, pots and pans, CDs, movies, and books, but it wasn't until a few months ago that I realized what a great resource it is for food, in particular organic and natural foods.
Now of course you cannot buy fresh produce over the internet, but for pantry staples and hard-to-find ingredients it is the place to go. Last month I ordered coconut oil for a much better price than I can find in the stores around here and just last week I ordered 12 cans of organic oatmeal. I bought a case of old-fashioned oats for slightly less than what I pay for conventional and then I ordered a case of steel cut oats for half the price of regular, conventional oats in the store. What made the deal even better is that products ordered directly from Amazon are eligible for free shipping if your order is over $25!
Many prodcuts also have a "Subscribe & Save" option where you can order a product once and continue to have it shipped to your door every month at a 15% reduced price. This would be good for products that you use on a regular basis.
You can further reduce your cost for food from Amazon by paying with Swagbucks.
Really, if you have never taken a look at the groceries on Amazon before, I suggest you go do it now. Unless that is, you don't like saving money.