Bob Sirott listed his 5 favorites with the closing of the Berghoff and the death of Marshall Fields as a backdrop. I have a hard time finding fault with it, as it looks like my own (though I'd go with the Co-op over 57th Street books).
Manny's
La Unica
Gene & Georgetti
Margie's
57th Street
I thought La Unica was especially nice, as it somehow remains relatively unknown to popular culture in Chicago. Of course, Sirott's wife Marianne Murciano is Cuban and every Cuban in Chicago goes to La Unica.
http://www.nbc5.com/entertainment/6256741/detail.html