I don't think anyone has mentioned the Mariano's grocery in Greektown, where one can certainly find lots of good, fresh food (including cooked meats, prepared salads, and such) to take and eat.
At Block 37, on Dearborn, is Latinicity with numerous eatery selections. Or, a little further across the river is the Italian equivalent, Eataly.
I'm always surprised that no one ever seems to recommend the Randolph Street restaurant district on this forum, considering how it is one of the most notable food hot spots in the city (and, really, just slightly further than Greektown.)
If one cares to journey a little further, you could easily get to Taylor Street, with all of its selections. (Have some Italian Ice, for goodness sake. It's the best!)
Or hop on the Blue Line to Wicker Park, with its restaurants.
Take the Red Line north and explore interesting eateries around Boystown. Ride south, instead, and you're quickly in Chinatown. Further north, at Argyle, will lead you to even more Asian restaurants in another noted district. And Andersonville has some interesting bread and circuses, also.
Of course, if you want a true Chicago place, with an eclectic variety of locals, head to Bari for an Italian Sub.
Edited by NorthShore, 11 August 2017 - 10:47 AM.