Hanukah is not such a big deal holiday -- I don't think I've ever seen a Hanukah menu, and I've lived most of my life in relatively high population Jewish areas. There is no special Hanukah dinner or foods beyond latkes and sufganiyot (jelly donuts), which some restaurants might add to their menus. Most Jews tend to celebrate at home, or they may carry out from one of the many Jewish/kosher caterers or stores. Suffice to say, I doubt there is much demand for a Hanukah menu!
I'd seek out those places that already feature deli style food (Eleven City Diner, Manny's). I'm not familiar with the western burbs to be able to offer suggestions. Up on the North Shore, Max and Benny's (Northbrook), Max's (Highland Park), or possibly L.Woods (Lincolnwood) might be options.
There is only one true kosher restaurant downtown, MetroKlub, and it is just open for lunch M-Th. You could call to see if they are doing anything for Hanukah.
MetroKlub
733 W. Madison
(312) 602-2104
"You should eat!"