|Looking for the Food City circular for Food City weekly ad specials? TheThriftyConsumer.com is dedicated to helping consumers save money on groceries by displaying the current Food City flyer. Below is the latest Food City weekly sales flyer / Food City circular. Weekly specials and weekly flyers for other grocery stores can be found here as well. TheThriftyConsumer.com is designed to show you the latest Food City sales flyer and Food City weekly specials so bookmark this page and check back before going grocery shopping.