I actually do a combination of things with my grocery purchases. I always buy all bread products at the Flowers bakery outlet. They always have the onion & kaiser rolls I like and the 9 or 12 or 13 grain bread for less than half than any grocery, and it's only half a block out of the way from my usual route home from work.
I get most of the staples -- graham crackers, grape juice, saltines, oatmeal,generic cheerios, biscuits, butter, fish planks, chicken, potpies at the Sav-A-Lot, which is only about 20 blocks S of my house. All the rest I usually get at the Publix, because unlike the Winn Dixie (my old neighbor called it the Dim Pixie) I won't have to wait forever in line, there store brands are excellent (Winn Dixie's --especially thrifty maid--suck) and the don't stick me to use their ATM. About once a month I stop by the new Wallyworld and buy a few things the other stores don't have: their ersatz version of Crystal Lite and Helluva Good Extra Sharp Cheddar. There is a 99¢ Stuff store I go by every month or so to pick up cheap Argentine and Chilean and other stuff.
Fresh veggies I always pick up on Thursday or Friday at the Opa-Locka Hialeah Flea market, because they are less than half the price of any market. This is tomato season in Fla, and you can get up to 5 pounds for a dollar.