The Egg Store down on Halsted in Bridgeport also has an interesting, but not always reliable produce selection.
3008 S. Halsted
I personally prefer Cermak Produce. Whole Foods will be a nice addition, despite whatever nightmares that mall is going to wreak on traffic at Canal and Roosevelt.
There's also the Maxwell Market (every Sunday) produce stands--mostly Mexican standards (cilantro, onions, cheeeeap avocados, dried beans galore, tomatillos, papaya), but there's always a vendor selling bulk boxes/crates/flats of fruit (strawberries, mangoes, kiwis, etc.) on the north side of Roosevelt.
The lack of a diverse selection of high quality produce is definitely a problem in the area, and is the main reason I signed up for a Spring CSA (community supported agriculture) subscription...and will sign up for a Summer subscription.
Welcome to the neighborhood!