That's a very broad question. Imagine if someone asked the same thing of you about New York City!
Can you narrow it down in some way? What neighborhood(s) do you expect to be in? Any particular kind of cuisine? Are you looking for a money-no-object gourmet fantasy, or something ethnic, etc? Perhaps you'd care for some real Chicago pizza, either the double-crust stuffed pizza at Giordano's ( www.giordanos.com ) or the deep-dish thick-crust pizza at Lou Malnati's ( www.loumalnatis.com )? Give us some guidance regarding what you're looking for...
Neighborhood spots - by this I mean that they are not necessarily a destination - if I don't live near one, I may not go out of my way to go to it. Good food, though.
1851 W. Addison St.
1769 W. Sunnyside Ave.
2537 N. Kedzie Blvd.
Hip spots - not as much known for their food as their atmosphere. This does not mean bad food, but definitely more of a place to look at the people around you.
Bin Wine Cafe
1559 N. Milwaukee Ave.
1520 N. Damen Ave.
465 E. Illinois St.