through Chicago or circumvent?

I would definitely go around Chicago unless there was something in particular that I wanted to see or do in the city.

From New York state, I would give consideration to skipping Illinois entirely and going across Canada to either the lower or upper peninsula of Michigan, and thence to Wisconsin. If money is not particularly tight the SS Badger ferry might be a fun option to get from Ludington, MI to Manitowoc, WI.

Going through did not work well for Clark Griswold.

Go around for sure no matter the day of the week take 80 west to I39 north

General big city - Sundays are usually good for driving through a big city UNLESS there is a big event (football, etc).

Weekdays are also acceptable IF you get there BEFORE rush hour (about 6AM) or after rush hour (about 7PM). I have done Cincinnati several times in the middle of the day. Not too bad !

I can't tell you on which route, but I went through Chicago headed north last year and the condition of the roads and bridges was far worse than the traffic. I won't go through there again.

Bill