1) Costco -- good for stocking up on what you'll use. Love their deal on yeast. Yes, you can take a bus, and they will let you in the store with a backpack on.
2) Trader Joe's -- because it's awesome (check out the threads in Chains)
3) Aldis -- Trader Joe's without the hype
4) Whole Foods -- "whole paycheck"
5) Giant Eagle
I also love visiting the ethnic stores. Shadyside has Japanese, Squirrel Hill has Korean, Oakland does indian -- and the Strip does Everything!
I go mainly to the Shadyside Market District because it's close.
I like Penn Avenue Fish Company for fish (and, since I'm there, lunch).
I get my Parmigiano-Reggiano @ Pennsylvania Macaroni (PennMac), and lots of other Italian specialties.
Whole Foods has the best price on olive oil and St. Andre ($9.99/lb). I like their Italian bread, too.
Trader Joe's is good for English Breakfast tea bags for ice tea. Their St. Andre is also $9.99, but you have to make sure it's not overly ammoniated (green-gray around the edges).
For day-to-day perishable items, I like to go to Whole Foods. I do go to Market District Giant Eagle too for more extensive selection and their weekly sale. Now that Aldi's is open a block from that Giant Eagle, I might start going there too, namely for the chocolate hazelnut spread.
I go to Bombay Mart (on Centre and Craig) every a couple of months for Brown Basmathi Rice (10lb ) and Frozen Paratha. They do have nice selection of Indian produce like curry leaves and fenugreek leaves.
On top of that, I do go to the Strip once or twice a month. I get my meat from Salem's; Flour Tortilla from Reyna; Ram Leaves & Wira Palm Sugar/Palm Candy from this Asian Store that only accepts cash ( I cannot think what it is called, Asian Market maybe?) . And Fresh tofu from Lotus, along with other items for Asian food.
So yeah, I go everywhere for groceries. Some people like Trader Joe's, but I'm not a big fan of prepackaged produce. Oh, if you're in Bloomfield, they do have nice Italian Grocery stores (one on Liberty and another one on the side street).