A companion idea to seasonal shopping is local shopping. Local shopping is buying foods that are grown or produced locally, which are often cheaper. For instance, when we lived in Michigan, we bought fresh locally produced apple cider every fall for much cheaper than I've seen it elsewhere. In our area of Texas, we can get 60 corn tortillas for $2. Really good salsa, avocados, peppers and similar things are also reasonably priced locally.
Don't forget local pick-your-own operations. Some of them are pretty outrageously priced, but others are a great deal for an hour or two of your work. I remember taking my older child out to pick blueberries at one near us in MI (for about 2/3 the cost of buying them at the best price in the store) with the younger child in a baby pack on my back. It was an exciting adventure for the older child, we got delicious fresh berries, and the younger child happily babbled at us while we picked. This is a particularly good idea if you like to can or freeze your own produce.
Another strategy is to find someone who grows their own and may have surplus from time to time. They may be willing to part with that surplus for a good price or even for bartered help with their garden. If you live in a rural area, get to know your neighbors and who is growing or raising what. If you can find someone who keeps their own chickens for eggs, fresh eggs from yard-raised hens have a taste that the store eggs (usually stored until almost too old to sell) can't begin to compare with. If someone raises livestock, you may be able to get a bargain on meat. My parents used to make a deal with friends of theirs to split the cost of the friends raising a calf each year in exchange for a share of the beef (between an acre garden and this, we had two freezers full of food all the time and shelves filled with home-canned vegetables and fruits).
And don't forget hunters and fishermen. Some may have more meat than they can use, and while laws may preclude selling it, they can give it away. I once worked for a delightful outdoorsman who made the most incredible venison jerky you can imagine, and he brought in bags of it to work to give away. If you know one who's generous like that, show your appreciation by offering to keep a pet or check their mail or water their plants when they're out of town.