With what the previous two posters have said, you'll should have no problems.
When I was on active duty at Fort Campbell, KY, I would drive the entire state of IL pretty often to get home to WI. I never wanted to test anything, so I disassembled my G19 and put it in a locked case in either the trunk of the car or the truck box in the bed of the pickup.
I was pulled over more than I'd care to talk about, couple speeding tickets...never once searched or questioned about more than the traffic stop - even with a car full of my deer hunting orange and other equipment.
Outside of Chicago, folks are regular folks and are just like people any other place who don't have an extreme, irrational anti-gun bias.