I've found pretty good ingredients at Del Ray on North Ave near 15th Ave in Melrose Park as well as the one on Grand Ave and Naragansett in Chicago.
In addition to mainly Hipano-centric produce, they occasionally have rotisserie chicken on sale for $2.99 - (normally $4.99) pretty good, seasoned with paprika and garlic powder...also small bags of mesquite charcoal, great dried chiles, dried beans, rice, etc.
Heartily second Caputo's in Elmwood Park on Harlem.
Don't pass up Caputo's Cheese on 15th Ave (North of North Ave) in Melrose Park as another great place to shop. Naturally, cheeses, (fresh mozzarella and ricotta every day), proscuitto (Parma is $9.99 / lb!), olives, dried pasta, salt-packed anchovies and capers, fresh sausage, arancini (on the weekends), cheap spices and a more than a few interesting inexpensive wines. The produce section is a bit spotty, at best.