I always like visiting grocery stores when traveling, you can find some interesting things to eat and occasionally something to bring back for friends and family.
Just south of Juarez Avenue on highway 307 is Chedraui, a large supermercado selling groceries, liquor, some clothes, small appliances, household products, etc. There's also a small prepared food section where you can get tacos and other things to eat while in the store.
There's at least two other large grocery stores now, one along the highway south of Juarez Avenue (can't remember the name but it's in the strip mall with Woolworth's) and another one which I think it called Mega and, regrettably, a WalMart which I have never come across.
What to buy: The liquor selection wasn't huge but the prices were much better than along 5th Avenue. There weren't as many choices for tequila but we found a good bottle for about 30% less than in town and a bottle of Bacardi Oro for my sister in law who said you couldn't buy it in the US.
It's the big grocery store in town and worth the trip to pick up the stuff you'll need. i generally pick up some toilletries once i get there to travel more lightly. It's nice to experience shopping as a local. and don't bother driving. it's a nice walk down bustling Juarez to hwy 337. You'll see stuff along the way that you'll want to come back to during your visit.
What to buy: becuase the pillows are sometimes musty in MX i pick up a cheap pillow. They have bedding, cheap clothes, etc. their sausage and cheese section is great and fresh. veggies are better at small markets. the only place in town to get fresh (in a bottle/jug) milk is sam's club. still only the boxed milk here :).
What to pay: cheap groceries - not much.